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Journal articles on the topic 'Periodic cusp wave'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Meng, Qing, and Bin He. "Exact Peakon, Compacton, Solitary Wave, and Periodic Wave Solutions for a Generalized KdV Equation." Mathematical Problems in Engineering 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/602432.

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We employ the approaches of both dynamical system and numerical simulation to investigate a generalized KdV equation, which is presented by Yin (2012). Some peakon, compacton, solitary wave, smooth periodic wave, and periodic cusp wave solutions are obtained, and the planar graphs of the compactons and the periodic cusp waves are simulated.

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2

Xie, Shaolong, and Bin Gao. "EXACT PERIODIC WAVE SOLUTIONS OF A SINGULAR INTEGRABLE EQUATION." Mathematical Modelling and Analysis 16, no. 1 (2011): 315–25. http://dx.doi.org/10.3846/13926292.2011.580788.

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In this paper, theory of dynamical systems is employed to investigate periodic waves of a singular integrable equation. These periodic waves contain smooth periodic waves, periodic cusp waves and periodic cusp loop waves. Under fixed parameter conditions, their exact parametric expressions are given.

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3

Long, Yao, and Can Chen. "Existence Analysis of Traveling Wave Solutions for a Generalization of KdV Equation." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/462957.

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By using the bifurcation theory of dynamic system, a generalization of KdV equation was studied. According to the analysis of the phase portraits, the existence of solitary wave, cusp wave, periodic wave, periodic cusp wave, and compactons were discussed. In some parametric conditions, exact traveling wave solutions of this generalization of the KdV equation, which are different from those exact solutions in existing references, were given.

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4

Fan, Feiting, and Xingwu Chen. "Dynamical behavior of traveling waves in a generalized VP-mVP equation with non-homogeneous power law nonlinearity." AIMS Mathematics 8, no. 8 (2023): 17514–38. http://dx.doi.org/10.3934/math.2023895.

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<abstract><p>In this paper, we investigate the dynamical behavior of traveling waves for a generalized Vakhnenko-Parkes-modified Vakhnenko-Parkes (VP-mVP) equation with non-homogeneous power law nonlinearity. By the dynamical systems approach and the singular traveling wave theory, the existence of all possible bounded traveling wave solutions is discussed, including smooth solutions (solitary wave solutions, periodic wave solutions and breaking wave solutions) and non-smooth solutions (solitary cusp wave solutions and periodic cusp wave solutions). We not only obtain all the expli

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5

DENG, SHENGFU, BOLING GUO, and TINGCHUN WANG. "SOME TRAVELING WAVE SOLITONS OF THE GREEN–NAGHDI SYSTEM." International Journal of Bifurcation and Chaos 21, no. 02 (2011): 575–85. http://dx.doi.org/10.1142/s0218127411028623.

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The traveling wave solutions for an equivalent system of the Green–Naghdi system are considered. The qualitative analysis methods of planar autonomous systems yield their phase portraits. The exact expressions of smooth soliton wave solutions, cusp soliton wave solutions, smooth periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given. These reveal some new properties of the Green–Naghdi system.

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6

Meng, Qing, and Bin He. "Bounded Traveling Wave Solutions and Their Relations for the Generalized HD Type Equation." Discrete Dynamics in Nature and Society 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/5383527.

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The generalized HD type equation is studied by using the bifurcation method of dynamical systems. From a dynamic point of view, the existence of different kinds of traveling waves which include periodic loop soliton, periodic cusp wave, smooth periodic wave, loop soliton, cuspon, smooth solitary wave, and kink-like wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. Also, all possible exact parametric representations of the bounded waves are presented and their relations are stated.

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7

LIU, ZHENGRONG, ALI MOHAMMED KAYED, and CAN CHEN. "PERIODIC WAVES AND THEIR LIMITS FOR THE CAMASSA–HOLM EQUATION." International Journal of Bifurcation and Chaos 16, no. 08 (2006): 2261–74. http://dx.doi.org/10.1142/s0218127406016045.

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In this paper, the bifurcation method of dynamical systems is employed to study the Camassa–Holm equation [Formula: see text] We investigate the periodic wave solutions of form u = φ(ξ) which satisfy φ(ξ + T) = φ(ξ), here ξ = x - ct and c, T are constants. Their six implicit expressions and two explicit expressions are obtained. We point out that when the initial values are changed, the periodic waves may become three waves, periodic cusp waves, smooth solitary waves and peakons. Our results give an explanation to the appearance of periodic cusp waves and peakons. Moreover, three sets of graph

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8

He, Bin, Qing Meng, Jinhua Zhang, and Yao Long. "Periodic Loop Solutions and Their Limit Forms for the Kudryashov-Sinelshchikov Equation." Mathematical Problems in Engineering 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/320163.

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The Kudryashov-Sinelshchikov equation is studied by using the bifurcation method of dynamical systems and the method of phase portraits analysis. We show that the limit forms of periodic loop solutions contain loop soliton solutions, smooth periodic wave solutions, and periodic cusp wave solutions. Also, some new exact travelling wave solutions are presented through some special phase orbits.

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Chen, Can, Weiguo Rui, and Yao Long. "Different Kinds of Singular and Nonsingular Exact Traveling Wave Solutions of the Kudryashov-Sinelshchikov Equation in the Special Parametric Conditions." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/456964.

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In this paper, by using the integral bifurcation method, we studied the Kudryashov-Sinelshchikov equation. In the special parametric conditions, some singular and nonsingular exact traveling wave solutions, such as periodic cusp-wave solutions, periodic loop-wave solutions, smooth loop-soliton solutions, smooth solitary wave solutions, periodic double wave solutions, periodic compacton solutions, and nonsmooth peakon solutions are obtained. Further more, the dynamic behaviors of these exact traveling wave solutions are investigated. It is found that the waveforms of some traveling wave solutio

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10

Li, Jibin, and Lin Jiang. "Exact Solutions and Bifurcations of a Modulated Equation in a Discrete Nonlinear Electrical Transmission Line (I)." International Journal of Bifurcation and Chaos 25, no. 01 (2015): 1550016. http://dx.doi.org/10.1142/s0218127415500169.

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In this paper, we consider a model which is a modulated equation in a discrete nonlinear electrical transmission line. By investigating the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we derive all explicit exact parametric representations of solutions (including smooth solitary wave solutions, smooth periodic wave solutions, peakons, compactons, periodic cusp wave solutions, etc.) under different parameter conditions.

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11

Kato, Kazuki, Masao Mori, and Go Ogiya. "Connection between cusp-core problem and too-big-to-fail problem in CDM model." Proceedings of the International Astronomical Union 11, S317 (2015): 312–13. http://dx.doi.org/10.1017/s174392131500705x.

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AbstractThe standard paradigm of structure formation in the universe, the cold dark matter cosmology, contains several crucial unsolved problems such as “cusp-core problem” and “too-big-to-fail problem”. To solve these problems, we study about the dynamical response of a virialized system with a central cusp to the energy feedback driven by periodic supernova feedback using collisionless N-body simulations with the Nested-Particle-Mesh code. The resonance between dark matter particles and the density wave excited by the oscillating potential plays a significant role in the cusp-core transition

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12

Fan, Xinghua, and Shasha Li. "Bifurcation of Traveling Wave Solutions of the Dual Ito Equation." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/153139.

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The dual Ito equation can be seen as a two-component generalization of the well-known Camassa-Holm equation. By using the theory of planar dynamical system, we study the existence of its traveling wave solutions. We find that the dual Ito equation has smooth solitary wave solutions, smooth periodic wave solutions, and periodic cusp solutions. Parameter conditions are given to guarantee the existence.

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13

Li, Jibin, and Zhijun Qiao. "Bifurcation and Traveling Wave Solutions for the Fokas Equation." International Journal of Bifurcation and Chaos 25, no. 10 (2015): 1550136. http://dx.doi.org/10.1142/s0218127415501369.

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This paper is devoted to discussing bifurcation and traveling wave solutions for the Fokas equation. By investigating the dynamical behavior with phase space analysis, we may derive all possible exact traveling wave solutions, including compactons, cuspons, periodic cusp wave solutions, and smooth solitary wave solutions.

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14

DODD, NICHOLAS, ADAM M. STOKER, DANIEL CALVETE, and ANURAK SRIARIYAWAT. "On beach cusp formation." Journal of Fluid Mechanics 597 (February 1, 2008): 145–69. http://dx.doi.org/10.1017/s002211200700972x.

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A system of shallow water equations and a bed evolution equation are used to examine the evolution of perturbations on an erodible, initially plane beach subject to normal wave incidence. Both a permeable (under Darcy's law) and an impermeable beach are considered. It is found that alongshore-periodic morphological features reminiscent of swash beach cusps form after a number of incident wave periods on both beaches. On the permeable (impermeable) beach these patterns are accretional (erosional). In both cases flow is ‘horn divergent’. Spacings of the cusps are consistent with observations, an

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15

Wen, Zhenshu. "Bifurcation of Traveling Wave Solutions for a Two-Component Generalizedθ-Equation". Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/597431.

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We study the bifurcation of traveling wave solutions for a two-component generalizedθ-equation. We show all the explicit bifurcation parametric conditions and all possible phase portraits of the system. Especially, the explicit conditions, under which there exist kink (or antikink) solutions, are given. Additionally, not only solitons and kink (antikink) solutions, but also peakons and periodic cusp waves with explicit expressions, are obtained.

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16

Cai, Qiue, Kaixuan Tan, and Jiang Li. "Bifurcations and exact traveling wave solutions for the regularized Schamel equation." Open Mathematics 19, no. 1 (2021): 1699–712. http://dx.doi.org/10.1515/math-2021-0136.

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Abstract In the present paper, we focus on studying the bifurcations and the traveling wave solutions (TWSs) for the regularized Schamel equation. Based on the bifurcation method of a dynamical system, a complete phase portrait analysis is given in various parameter conditions and some novel TWSs with the same energy of the Hamiltonian system are discovered. Various significant results on exact expressions of TWSs, including solitary waves, periodic waves, cusp waves, weak kink waves, loop solitons, compactons in different conditions are obtained.

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17

Shi, Jianping, and Jibin Li. "Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/893279.

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The paper considers the nonlocal hydrodynamic-type systems which are two-dimensional travelling wave systems with a five-parameter group. We apply the method of dynamical systems to investigate the bifurcations of phase portraits depending on the parameters of systems and analyze the dynamical behavior of the travelling wave solutions. The existence of peakons, compactons, and periodic cusp wave solutions is discussed. When the parameternequals 2, namely, let the isochoric Gruneisen coefficient equal 1, some exact analytical solutions such as smooth bright solitary wave solution, smooth and no

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18

Li, Jibin, and Fengjuan Chen. "Bifurcations and Exact Solutions of a Modulated Equation in a Discrete Nonlinear Electrical Transmission Line (II)." International Journal of Bifurcation and Chaos 25, no. 03 (2015): 1550045. http://dx.doi.org/10.1142/s0218127415500455.

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In this paper, we consider a model which is the modulated equation in a discrete nonlinear electrical transmission line. This model is an integrable planar dynamical system having three singular straight lines. By using the theory of singular systems and investigating the dynamical behavior, we obtain bifurcations of the phase portraits of the system under different parameter conditions. Corresponding to some special level curves, we derive possible exact explicit parametric representations of solutions (including smooth solitary wave and periodic wave solutions, periodic cusp wave solutions)

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19

LI, JIBIN, and ZHIJUN QIAO. "BIFURCATIONS AND EXACT TRAVELING WAVE SOLUTIONS OF THE GENERALIZED TWO-COMPONENT CAMASSA–HOLM EQUATION." International Journal of Bifurcation and Chaos 22, no. 12 (2012): 1250305. http://dx.doi.org/10.1142/s0218127412503051.

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In this paper, we apply the method of dynamical systems to a generalized two-component Camassa–Holm system. Through analysis, we obtain solitary wave solutions, kink and anti-kink wave solutions, cusp wave solutions, breaking wave solutions, and smooth and nonsmooth periodic wave solutions. To guarantee the existence of these solutions, we give constraint conditions among the parameters associated with the generalized Camassa–Holm system. Choosing some special parameters, we obtain exact parametric representations of the traveling wave solutions.

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20

Li, Jibin. "Exact Explicit Peakon and Periodic Cusp Wave Solutions for Several Nonlinear Wave Equations." Journal of Dynamics and Differential Equations 20, no. 4 (2008): 909–22. http://dx.doi.org/10.1007/s10884-008-9114-5.

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21

McKenzie, J. F., and T. B. Doyle. "Trans-sonic cusped shaped, periodic waves and solitary waves of the electrostatic ion-cyclotron type." Nonlinear Processes in Geophysics 11, no. 4 (2004): 421–25. http://dx.doi.org/10.5194/npg-11-421-2004.

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Abstract. By adopting an essentially fluid dynamic viewpoint we derive the wave structure equation for stationary, fully nonlinear, electrostatic, ion-cyclotron waves. The existence of two fundamental constants of the motion, namely, conservation of momentum flux parallel to the ambient magnetic field, and energy flux parallel to the direction of wave propagation, enables the wave structure equation to be reduced to a first order differential equation, which has solutions that are physically transparent. The analysis shows that sufficiently oblique waves, propagating at sub-ion acoustic speeds

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22

Uddin, Sabur, Shazia Karim, F. S. Alshammari, et al. "Bifurcation Analysis of Travelling Waves and Multi-rogue Wave Solutions for a Nonlinear Pseudo-Parabolic Model of Visco-Elastic Kelvin-Voigt Fluid." Mathematical Problems in Engineering 2022 (September 27, 2022): 1–16. http://dx.doi.org/10.1155/2022/8227124.

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Through this article, we focus on the extension of travelling wave solutions for a prevalent nonlinear pseudo-parabolic physical Oskolkov model for Kevin-Voigt fluids by using two integral techniques. First of all, we explore the bifurcation and phase portraits of the model for different parametric conditions via a dynamical system approach. We derive smooth waves of the bright bell and dark bell, periodic waves, and singular waves of dark and bright cusps, in correspondence to homoclinic, periodic, and open orbits with cusp, respectively. Each orbit of the phase portraits is envisaged through

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23

GUO, B., and Z. LIU. "Periodic cusp wave solutions and single-solitons for the b-equation☆." Chaos, Solitons & Fractals 23, no. 4 (2005): 1451–63. http://dx.doi.org/10.1016/s0960-0779(04)00402-3.

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24

Guo, Boling, and Zhengrong Liu. "Periodic cusp wave solutions and single-solitons for the b-equation." Chaos, Solitons & Fractals 23, no. 4 (2005): 1451–63. http://dx.doi.org/10.1016/j.chaos.2004.06.062.

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25

Jaradat, Imad, Marwan Alquran, Sania Qureshi, Tukur A. Sulaiman, and Abdullahi Yusuf. "Convex-rogue, half-kink, cusp-soliton and other bidirectional wave-solutions to the generalized Pochhammer-Chree equation." Physica Scripta 97, no. 5 (2022): 055203. http://dx.doi.org/10.1088/1402-4896/ac5f25.

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Abstract The generalized Pochhammer-Chree equation is considered and studied for different orders of its nonlinearity terms The Kudryashov-expansion method is used and bidirectional kink, singular-kink, rogue-periodic, and V-shaped wave-solutions are obtained. Moreover, we modify the sine-cosine function method to accommodate the current model and obtain symmetric half-kink, convex-rogue, and cusp bidirectional waves. On the other side, a graphical analysis is conducted to identify the physical shapes of the obtained solutions to the proposed model. Finally, the polynomial function method is i

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26

Li, Jibin, and Fengjuan Chen. "Exact Solutions and Bifurcations of a Modulated Equation in a Discrete Nonlinear Electrical Transmission Line (III)." International Journal of Bifurcation and Chaos 26, no. 01 (2016): 1650011. http://dx.doi.org/10.1142/s0218127416500115.

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In this paper, we consider a modulated equation in a discrete nonlinear electrical transmission line. This model is an integrable planar dynamical system having three singular straight lines. By using the theory of singular systems to investigate the dynamical behavior for this system, we obtain bifurcations of phase portraits under different parameter conditions. Corresponding to some special level curves, we derive exact explicit parametric representations of solutions (including smooth solitary wave solutions, peakons, compactons, periodic cusp wave solutions) under different parameter cond

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27

Xie, Shaolong, and Jionghui Cai. "Exact periodic, cusp, solitary and loop wave solutions of the EX-ROE." International Journal of Computer Mathematics 88, no. 13 (2011): 2824–37. http://dx.doi.org/10.1080/00207160.2011.559228.

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28

Zhou, Jiangbo, and Lixin Tian. "Solitons, peakons and periodic cusp wave solutions for the Fornberg–Whitham equation." Nonlinear Analysis: Real World Applications 11, no. 1 (2010): 356–63. http://dx.doi.org/10.1016/j.nonrwa.2008.11.014.

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29

Zhang, Lijun, Li-Qun Chen, and Xuwen Huo. "Peakons and periodic cusp wave solutions in a generalized Camassa–Holm equation." Chaos, Solitons & Fractals 30, no. 5 (2006): 1238–49. http://dx.doi.org/10.1016/j.chaos.2005.08.202.

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Wen, Zhenshu. "Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham Equation." Abstract and Applied Analysis 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/704931.

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Fan et al. studied the bifurcations of traveling wave solutions for a two-component Fornberg-Whitham equation. They gave a part of possible phase portraits and obtained some uncertain parametric conditions for solitons and kink (antikink) solutions. However, the exact explicit parametric conditions have not been given for the existence of solitons and kink (antikink) solutions. In this paper, we study the bifurcations for the two-component Fornberg-Whitham equation in detalis, present all possible phase portraits, and give the exact explicit parametric conditions for various solutions. In addi

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Sabi’u, Jamilu, Mustafa Inc, Temesgen Leta, Dumitru Baleanu, and Hadi Rezazadeh. "Dynamical behaviour of the Joseph-Egri equation." Thermal Science 27, Spec. issue 1 (2023): 19–28. http://dx.doi.org/10.2298/tsci23s1019s.

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We investigate traveling wave solutions to the Joseph-Egri equation via extended auxiliary equation technique. We have determined stationary points of the dynamical systems by using bifurcation method. We also acquire cusp, periodic and homoclinic orbits. The investigated solutions are entirely different from the reported in the liter?ature. However, some of the reported solutions are plotted to understand the physical application of the considered model using renowned mathematical software.

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Qiao, Li-Jing, Sheng-Qiang Tang, and Hai-Xia Zhao. "Single Peak Soliton and Periodic Cusp Wave of the Generalized Schrodinger–Boussinesq Equations." Communications in Theoretical Physics 63, no. 6 (2015): 731–42. http://dx.doi.org/10.1088/0253-6102/63/6/731.

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Zeng, Libing. "Solitary Wave, Periodic Cusp Wave and Compactons of the (2+1)-Dimensional KP-Like K(m,n) Equation." British Journal of Mathematics & Computer Science 2, no. 3 (2012): 163–75. http://dx.doi.org/10.9734/bjmcs/2012/1420.

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Li, Jibin, and Yi Zhang. "Exact loop solutions, cusp solutions, solitary wave solutions and periodic wave solutions for the special CH–DP equation." Nonlinear Analysis: Real World Applications 10, no. 4 (2009): 2502–7. http://dx.doi.org/10.1016/j.nonrwa.2008.05.006.

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Yusupov, Kamil M., and Nataliya V. Bakhmetieva. "Sporadic E Layer with a Structure of Double Cusp in the Vertical Sounding Ionogram." Atmosphere 12, no. 9 (2021): 1093. http://dx.doi.org/10.3390/atmos12091093.

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In this study, we analyzed a large number of vertical sounding ionograms, obtained by the mid-latitude Cyclone ionosonde (55.85° N; 48.8° E) of Kazan (Volga Region) Federal University, which operates in a rapid-run mode of ionograms (1 ionogram per minute). Ionograms with a sporadic E layer type c, which have an unusual double cusp on the trace from the sporadic layer, were found among them. We attempted to simulate this unusual double cusp trace shape. Model calculations were performed to clarify the reasons for the appearance of the double cusp and to determine the shape of the lower part of

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Doole, S. H., and J. Norbury. "The bifurcation of steady gravity water waves in (R, S) parameter space." Journal of Fluid Mechanics 302 (November 10, 1995): 287–305. http://dx.doi.org/10.1017/s0022112095004101.

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The bifurcation of steady periodic waves from irrotational inviscid streamflows is considered. Normalizing the flux Q to unity leaves two other natural quantities R (pressure head) and S (flowforce) to parameterize the wavetrain. In a well-known paper, Benjamin & Lighthill (1954) presented calculations within a cnoidal-wave theory which suggested that the corresponding values of R and S lie inside the cusped locus traced by the sub- and supercritical streamflows. This rule has been applied since to many other flow scenarios. In this paper, regular expansions for the streamfunction and prof

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Kuo, Spencer. "Linear and Nonlinear Plasma Processes in Ionospheric HF Heating." Plasma 4, no. 1 (2021): 108–44. http://dx.doi.org/10.3390/plasma4010008.

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Featured observations of high frequency (HF) heating experiments are first introduced; the uniqueness of each observation is presented; the likely cause and physical process of each observed phenomenon instigated by the HF heating are discussed. A special point in the observations, revealed through the ionograms, is the competition between the Langmuir parametric instability and upper hybrid parametric instability excited in the heating experiments and the impact of the natural cusp at foE (the peak plasma frequency of the ionospheric E region) on the competition. The ionograms also infer the

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MARSHALL, J. S. "The flow induced by periodic vortex rings wrapped around a columnar vortex core." Journal of Fluid Mechanics 345 (August 25, 1997): 1–30. http://dx.doi.org/10.1017/s0022112097005739.

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A study has been performed of the interaction of periodic vortex rings with a central columnar vortex, both for the case of identical vortex rings and the case of rings of alternating sign. Numerical calculations, both based on an adaptation of the Lundgren–Ashurst (1989) model for the columnar vortex dynamics and by numerical solution of the axisymmetric Navier–Stokes and Euler equations in the vorticity–velocity formulation using a viscous vorticity collocation method, are used to investigate the response of the columnar vortex to the ring-induced velocity field. In all cases, waves of varia

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Haixia Zhao, Lijing Qiao, and Shengqiang Tang. "PEAKON, PSEUDO-PEAKON, LOOP, AND PERIODIC CUSP WAVE SOLUTIONS OF A THREE-DIMENSIONAL 3DKP(2, 2) EQUATION WITH NONLINEAR DISPERSION." Journal of Applied Analysis & Computation 5, no. 3 (2015): 301–12. http://dx.doi.org/10.11948/2015027.

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Mann, I. R., I. Voronkov, M. Dunlop, et al. "Coordinated ground-based and Cluster observations of large amplitude global magnetospheric oscillations during a fast solar wind speed interval." Annales Geophysicae 20, no. 4 (2002): 405–26. http://dx.doi.org/10.5194/angeo-20-405-2002.

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Abstract. We present magnetospheric observations of very large amplitude global scale ULF waves, from 9 and 10 December 2000 when the upstream solar wind speed exceeded 600 km/s. We characterise these ULF waves using ground-based magnetometer, radar and optical instrumentation on both the dawn and dusk flanks; we find evidence to support the hypothesis that discrete frequency field line resonances (FLRs) were being driven by magnetospheric waveguide modes. During the early part of this interval, Cluster was on an outbound pass from the northern dusk side magnetospheric lobe into the magnetoshe

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Yasmin, Humaira, Haifa A. Alyousef, Sadia Asad, Imran Khan, R. T. Matoog, and S. A. El-Tantawy. "The Riccati-Bernoulli sub-optimal differential equation method for analyzing the fractional Dullin-Gottwald-Holm equation and modeling nonlinear waves in fluid mediums." AIMS Mathematics 9, no. 6 (2024): 16146–67. http://dx.doi.org/10.3934/math.2024781.

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<abstract><p>The present study investigates the fractional Dullin-Gottwald-Holm equation by using the Riccati-Bernoulli sub-optimal differential equation method with the Bäcklund transformation. By employing a well-established criterion, the present study reveals novel cusp soliton solutions that resemble peakons and offers valuable insights into their dynamic behaviors and mysterious phenomena. The solution family encompasses various analytical solutions, such as peakons, periodic, and kink-wave solutions. Furthermore, the impact of both the time- and space-fractional parameters o

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Cai, Huixian, Chaohong Pan, and Zhengrong Liu. "Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System." Abstract and Applied Analysis 2014 (2014): 1–20. http://dx.doi.org/10.1155/2014/189486.

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We study the bifurcations of nonlinear waves for the generalized Drinfel’d-Sokolov systemut+(vm)x=0,vt+a(vn)xxx+buxv+cuvx=0calledD(m,n)system. We reveal some interesting bifurcation phenomena as follows. (1) ForD(2,1)system, the fractional solitary waves can be bifurcated from the trigonometric periodic waves and the elliptic periodic waves, and the kink waves can be bifurcated from the solitary waves and the singular waves. (2) ForD(1,2)system, the compactons can be bifurcated from the solitary waves, and the peakons can be bifurcated from the solitary waves and the singular cusp waves. (3) F

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Qian, Tifei, and Minying Tang. "Peakons and periodic cusp waves in a generalized Camassa–Holm equation." Chaos, Solitons & Fractals 12, no. 7 (2001): 1347–60. http://dx.doi.org/10.1016/s0960-0779(00)00117-x.

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Wen, Zhenshu. "Bifurcation of solitons, peakons, and periodic cusp waves for $$\varvec{\theta }$$ θ -equation". Nonlinear Dynamics 77, № 1-2 (2014): 247–53. http://dx.doi.org/10.1007/s11071-014-1289-1.

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Wen, Zhenshu, and Zhengrong Liu. "Bifurcation of peakons and periodic cusp waves for the generalization of the Camassa–Holm equation." Nonlinear Analysis: Real World Applications 12, no. 3 (2011): 1698–707. http://dx.doi.org/10.1016/j.nonrwa.2010.11.002.

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Wen, Zhenshu. "Extension on peakons and periodic cusp waves for the generalization of the Camassa-Holm equation." Mathematical Methods in the Applied Sciences 38, no. 11 (2014): 2363–75. http://dx.doi.org/10.1002/mma.3226.

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Mondal, Sripan, Abhishek K. Srivastava, Sudheer K. Mishra, et al. "Reconnection-generated Plasma Flows in the Quasi-separatrix Layer in Localized Solar Corona." Astrophysical Journal 953, no. 1 (2023): 84. http://dx.doi.org/10.3847/1538-4357/acd2da.

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Abstract Multiwavelength observations of the propagating disturbances (PDs), discovered by Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO), are analyzed to determine their driving mechanism and physical nature. Two magnetic strands in the localized corona are observed to approach and merge with each other, followed by the generation of brightening, which further propagates in a cusp-shaped magnetic channel. Differential emission measure analysis shows an occurrence of heating in this region of interest. We extrapolate potential magnetic field lines at coronal heigh

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Chechulina, Iryna. "Попередній аналіз аттичної чорнолакової кераміки з експозиції Археологічного музею ІА НАН України / Attic Black-Glazed Pottery From the Collection of Exposition of the Archaeological Museum of IA NASU". VITA ANTIQUA 11 (20 грудня 2019): 166–72. https://doi.org/10.37098/VA-2019-11-166-172.

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Finds of Attic tableware and ceremonial ware in the North Black Sea region are mass, and that is why they are so important since they provide information for detailed chronology of ancient material. The collection of finds from Olbia, which is exhibited in the Archaeological Museum of IA NASU, is quite numerous. The investigated part of the material includes Attic black-glazed pottery, which was found in Olbia in different years at different sites of excavations, from 1962 to 2000. Some finds, unfortunately, have only museum archive numbers, so we are not able to trace their origin. All the ce

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Le, G., S. H. Chen, Y. Zheng, et al. "Coordinated polar spacecraft, geosynchronous spacecraft, and ground-based observations of magnetopause processes and their coupling to the ionosphere." Annales Geophysicae 22, no. 12 (2004): 4329–50. http://dx.doi.org/10.5194/angeo-22-4329-2004.

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Abstract. In this paper, we present in-situ observations of processes occurring at the magnetopause and vicinity, including surface waves, oscillatory magnetospheric field lines, and flux transfer events, and coordinated observations at geosynchronous orbit by the GOES spacecraft, and on the ground by CANOPUS and 210° Magnetic Meridian (210MM) magnetometer arrays. On 7 February 2002, during a high-speed solar wind stream, the Polar spacecraft was skimming the magnetopause in a post-noon meridian plane for ~3h. During this interval, it made two short excursions and a few partial crossings into

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Zeng, Libing, and Shengqiang Tang. "Solitary Wave, Periodic Cusp Wave and Compactons of the (2+1)-Dimensional KP-Like K(m,n) Equation." October 13, 2012. https://doi.org/10.5281/zenodo.9021.

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By using the bifurcation theory of dynamical systems to the generalized KP equation, under different parametric conditions, various sufficient conditions to guarantee the existence of the solitary wave solutions, periodic cusp wave solutions and compactons solutions are given. Some exact explicit parametric representations of the above waves are determined.

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