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Academic literature on the topic 'Soliton solutions'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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Journal articles on the topic "Soliton solutions"

1

Ma, Hongcai, Qiaoxin Cheng, and Aiping Deng. "N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation." Modern Physics Letters B 35, no. 10 (2021): 2150277. http://dx.doi.org/10.1142/s0217984921502778.

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[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the i

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2

Wang, Chunxia, Xiaojun Yin, and Liguo Chen. "Soliton molecules, bifurcation solitons and interaction solutions of a generalized (2 + 1)-dimensional korteweg-de vries system for the shallow-water waves." Physica Scripta 99, no. 10 (2024): 105272. http://dx.doi.org/10.1088/1402-4896/ad79a1.

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Abstract The central purpose of this paper is exploring the soliton molecules, bifurcation solitons and interaction solutions of the Korteweg–de Vries system based on the Hirota bilinear method. The studied system acts as an extension of the classic KdV system for the shallow-water waves, and is very useful to contribute in nonlinear wave phenomena. Firstly, the soliton molecules are obtained by adding resonance parameters in N-soliton. Then the interaction solutions between soliton/breather and soliton molecules are studied, as well as the interaction between two soliton molecules by using N-

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3

Sun, Ya, Bo Tian, Yu-Feng Wang, Yun-Po Wang, and Zhi-Ruo Huang. "Bright solitons and their interactions of the (3 + 1)-dimensional coupled nonlinear Schrödinger system for an optical fiber." Modern Physics Letters B 29, no. 35n36 (2015): 1550245. http://dx.doi.org/10.1142/s0217984915502450.

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Under investigation in this paper is the [Formula: see text]-dimensional coupled nonlinear Schrödinger system for an optical fiber with birefringence. With the Hirota method, bilinear forms of the system are derived via an auxiliary function, and the bright one- and two-soliton solutions are constructed. Based on those soliton solutions, soliton propagation and interaction are investigated analytically and graphically. Non-singular cases of the bright one-soliton solutions are presented, from which the single-peak and two-peak solitons can arise, respectively. Through the analysis on the brigh

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4

Hossain, Md Nur, M. Mamun Miah, Moataz Alosaimi, Faisal Alsharif, and Mohammad Kanan. "Exploring Novel Soliton Solutions to the Time-Fractional Coupled Drinfel’d–Sokolov–Wilson Equation in Industrial Engineering Using Two Efficient Techniques." Fractal and Fractional 8, no. 6 (2024): 352. http://dx.doi.org/10.3390/fractalfract8060352.

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The time-fractional coupled Drinfel’d–Sokolov–Wilson (DSW) equation is pivotal in soliton theory, especially for water wave mechanics. Its precise description of soliton phenomena in dispersive water waves makes it widely applicable in fluid dynamics and related fields like tsunami prediction, mathematical physics, and plasma physics. In this study, we present novel soliton solutions for the DSW equation, which significantly enhance the accuracy of describing soliton phenomena. To achieve these results, we employed two distinct methods to derive the solutions: the Sardar subequation method, wh

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5

Yıldırım, Y., and A. Biswas. "Dispersive optical soliton perturbation with multiplicative white noise having parabolic law of self-phase modulation." Semiconductor Physics, Quantum Electronics and Optoelectronics 28, no. 01 (2025): 053–58. https://doi.org/10.15407/spqeo28.01.053.

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In this paper, we investigate dispersive optical solitons incorporating multiplicative white noise. Utilizing the F-expansion procedure, we derive various soliton solutions, including dark soliton solutions, singular soliton solutions, bright soliton solutions, straddled singular-singular soliton solutions, complexiton solutions, and straddled dark-bright soliton solutions. Moreover, we discuss the parametric restrictions necessary for the existence of these soliton solutions, providing a comprehensive analysis of the conditions under which these solutions are valid. Our findings contribute to

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6

Ma, Hongcai, Huaiyu Huang, and Aiping Deng. "Soliton molecules and some novel hybrid solutions for (3+1)-dimensional B-type Kadomtsev–Petviashvili equation." Modern Physics Letters B 35, no. 23 (2021): 2150388. http://dx.doi.org/10.1142/s0217984921503887.

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In recent years, soliton molecules have received reinvigorating scientific interests in physics and other fields. Soliton molecules have been successfully found in optical experiments. In this paper, we attribute the solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by employing the bilinear method. Based on the [Formula: see text]-soliton solutions, we establish the soliton molecules, asymmetric solitons and some novel hybrid solutions of this equation by means of the velocity resonance mechanism and the long wave limit method. Finally, we give dynamic graphs of

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7

Ahmed, Iftikhar, Aly R. Seadawy, and Dianchen Lu. "Mixed lump-solitons, periodic lump and breather soliton solutions for (2 + 1)-dimensional extended Kadomtsev–Petviashvili dynamical equation." International Journal of Modern Physics B 33, no. 05 (2019): 1950019. http://dx.doi.org/10.1142/s021797921950019x.

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In this study, based on the Hirota bilinear method, mixed lump-solitons, periodic lump and breather soliton solutions are derived for (2 + 1)-dimensional extended KP equation with the aid of symbolic computation. Furthermore, dynamics of these solutions are explained with 3d plots and 2d contour plots by taking special choices of the involved parameters. Through the mixed lump-soliton solutions, we observe two fusion phenomena, first from interaction of lump and single soliton and other from interaction of lump with two solitons. In both cases, lump moves gradually towards soliton and transfer

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8

Asjad, Muhammad Imran, Naeem Ullah, Hamood Ur Rehman, and Tuan Nguyen Gia. "Novel soliton solutions to the Atangana–Baleanu fractional system of equations for the ISALWs." Open Physics 19, no. 1 (2021): 770–79. http://dx.doi.org/10.1515/phys-2021-0085.

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Abstract This work deals the construction of novel soliton solutions to the Atangana–Baleanu (AB) fractional system of equations for the ion sound and Langmuir waves by using Sardar-subequation method (SSM). The outcomes are in the form of bright, singular, dark and combo soliton solutions. These solutions have wide applications in the arena of optoelectronics and wave propagation. The bright solitons will be a vast advantage in controlling the soliton disorder, dark solitons are also beneficial for soliton communication when a background wave exists and singular solitons only elaborate the sh

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Huang, Qian-Min, and Yi-Tian Gao. "Bilinear form, bilinear Bäcklund transformation and dynamic features of the soliton solutions for a variable-coefficient (3+1)-dimensional generalized shallow water wave equation." Modern Physics Letters B 31, no. 22 (2017): 1750126. http://dx.doi.org/10.1142/s0217984917501263.

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Under investigation in this letter is a variable-coefficient (3[Formula: see text]+[Formula: see text]1)-dimensional generalized shallow water wave equation. Bilinear form and Bäcklund transformation are obtained. One-, two- and three-soliton solutions are derived via the Hirota bilinear method. Interaction and propagation of the solitons are discussed graphically. Stability of the solitons is studied numerically. Soliton amplitude is determined by the spectral parameters. Soliton velocity is not only related to the spectral parameters, but also to the variable coefficients. Phase shifts are t

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Yang, Hongwei, Yong Zhang, Xiaoen Zhang, Xin Chen, and Zhenhua Xu. "The Rational Solutions and Quasi-Periodic Wave Solutions as well as Interactions ofN-Soliton Solutions for 3 + 1 Dimensional Jimbo-Miwa Equation." Advances in Mathematical Physics 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/7241625.

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The exact rational solutions, quasi-periodic wave solutions, andN-soliton solutions of 3 + 1 dimensional Jimbo-Miwa equation are acquired, respectively, by using the Hirota method, whereafter the rational solutions are also called algebraic solitary waves solutions and used to describe the squall lines phenomenon and explained possible formation mechanism of the rainstorm formation which occur in the atmosphere, so the study on the rational solutions of soliton equations has potential application value in the atmosphere field; the soliton fission and fusion are described based on the resonant

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Dissertations / Theses on the topic "Soliton solutions"

1

Renger, Walter. "Limits of soliton solutions /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9823316.

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Sooman, Craig. "Soliton solutions of noncommutative integrable systems." Thesis, University of Glasgow, 2010. http://theses.gla.ac.uk/1449/.

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This thesis is concerned with solutions of noncommutative integrable systems where the noncommutativity arises through the dependent variables in either the hierarchy or Lax pair generating the equation. Both Chapters 1 and 2 are entirely made up of background material and contain no new material. Furthermore, these chapters are concerned with commutative equations. Chapter 1 outlines some of the basic concepts of integrable systems including historical attempts at finding solutions of the KdV equation, the Lax method and Hirota's direct method for finding multi-soliton solutions of an integra

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Reis, Philip Axel. "Soliton solutions to Calogero-Moser systems." Thesis, KTH, Fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-265631.

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4

Middlemas, Erin. "Soliton Solutions of the Nonlinear Schrödinger Equation." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/honors/66.

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The nonlinear Schrödinger equation is a classical field equation that describes weakly nonlinear wave-packets in one-dimensional physical systems. It is in a class of nonlinear partial differential equations that pertain to several physical and biological systems. In this project we apply a pseudo-spectral solution-estimation method to a modified version of the nonlinear Schrödinger equation as a means of searching for solutions that are solitons, where a soliton is a self-reinforcing solitary wave that maintains its shape over time. The pseudo-spectral method estimates solutions by utilizing

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Morrison, Alan James. "Soliton solutions of some novel nonlinear evolution equations." Thesis, University of Strathclyde, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248782.

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Makhankov, Vladimir, та Granados Máximo Agüero. "Bubbles Soliton Solutions in the φᶝ - Field Theory". Pontificia Universidad Católica del Perú, 2002. http://repositorio.pucp.edu.pe/index/handle/123456789/95741.

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Zhou, Yuan. "Lump, complexiton and algebro-geometric solutions to soliton equations." Scholar Commons, 2017. http://scholarcommons.usf.edu/etd/6988.

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In chapter 2, we study two Kaup-Newell-type matrix spectral problems, derive their soliton hierarchies within the zero curvature formulation, and furnish their bi-Hamiltonian structures by the trace identity to show that they are integrable in the Liouville sense. In chapter 5, we obtain the Riemann theta function representation of solutions for the first hierarchy of generalized Kaup-Newell systems. In chapter 3, using Hirota bilinear forms, we discuss positive quadratic polynomial solutions to generalized bilinear equations, which generate lump or lump-type solutions to nonlinear evolution e

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Allami, Mohammed Jabbar Hawas. "Soliton equations in two spatial dimensions and their solutions." Thesis, University of Kent, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.587561.

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This thesis concerns soliton equations in two spatial dimensions. Camassa and Holm derived a model of shallow water wave which continues to attract attention in the light of the remarkable wealth of mathematical and physical properties of its solutions. More recently, Kraenkel and Zenchuk introduced an extension of Camassa and Holm's equation to two spatial dimensions, with three fields, and derived it from a Lax pair. However, finding solutions of this model is more challenging. In order to understand and find solutions of the (2 + l)-dimensional Camassa- Holm (CH) equation, it turns out that

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Bury, Rhys Thomas. "Automorphic lie algebras, corresponding integrable systems and their soliton solutions." Thesis, University of Leeds, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.539708.

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陶福臻 and Fook-tsun To. "Soliton solutions to gravitational field and Yang-Mills gauge field." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31233910.

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Books on the topic "Soliton solutions"

1

Błaszak, Maciej. Theory of classical soliton particles. Wydawn. Nauk. UAM, 1989.

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Guo, Boling, Zaihui Gan, Linghai Kong, and Jingjun Zhang. The Zakharov System and its Soliton Solutions. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2582-2.

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3

Imbens, Hubertus Joannes. Finite dimensional solutions of hierarchies of soliton equations. Mathematical institute rijksuniversiteit, 1989.

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Imbens, Huib-Jan. Finite dimensional solutions of hierarchies of soliton equations =: Eindig dimensionale oplossingen van hie rarchiee n van soliton vergelijkingen. [s.n.], 1989.

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5

Gesztesy, Fritz. Soliton equations and their algebro-geometric solutions: (1+1)-dimensional discrete models. Cambridge University Press, 2008.

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6

Holden, Helge. Soliton Equations and Their Algebro-Geometric Solutions: Volume I: (1+1)-Dimensional Continuous Models. Cambridge University Press, 2003.

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7

Akhmediev, Nail N. Solitons: Nonlinear pulses and beams. Chapman & Hall, 1997.

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8

Börjesson, Susanne. SOLISOL-handling of solid solutions. Swedish Nuclear Power Inspectorate, 1992.

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9

Kashcheev, V. N. Ėvristicheskie metody poluchenii͡a︡ resheniĭ nelineĭnykh uravneniĭ solitoniki. "Zinatne", 1990.

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Gesztesy, Fritz. (m)KdV solitons on the background of quasi-periodic finite-gap solutions. American Mathematical Society, 1995.

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Book chapters on the topic "Soliton solutions"

1

Makhankov, Vladimir G. "The Existence of Soliton-Like Solutions." In Soliton Phenomenology. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-2217-4_10.

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2

Christ, N. H., and T. D. Lee. "Quantum expansion of soliton solutions." In Selected Papers. Birkhäuser Boston, 1986. http://dx.doi.org/10.1007/978-1-4612-5397-6_53.

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3

Enns, Richard H., and George C. McGuire. "Nonlinear PDE Models: Soliton Solutions." In Computer Algebra Recipes. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0171-4_14.

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Weideman, J. A. C. "Dynamics of Complex Singularities of Nonlinear PDEs." In SEMA SIMAI Springer Series. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-86236-7_13.

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AbstractSolutions to nonlinear evolution equations exhibit a wide range of interesting phenomena such as shocks, solitons, recurrence, and blow-up. As an aid to understanding some of these features, the solutions can be viewed as analytic functions of a complex space variable. The dynamics of poles and branch point singularities in the complex plane can often be associated with the aforementioned features of the solution. Some of the computational and analytical results in this area are surveyed here. This includes a first attempt at computing the poles in the famous Zabusky–Kruskal experiment

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Makhankov, Vladimir G. "The Class of Soliton Solutions to the Vector Version of the Nonlinear Schrödinger Equation With Self-Consistent Potentials." In Soliton Phenomenology. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-2217-4_9.

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Škrinjar, M., D. Kapor, and S. Stojanovic. "Davydov Ansatz and Proper Solutions of Schrödinger Equation for Fröhlich Hamiltonian." In Davydov’s Soliton Revisited. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-9948-4_8.

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Domrin, A. V. "Soliton Equations and Their Holomorphic Solutions." In Trends in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53305-2_22.

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Pietrzyk, M. E. "Propagation of Short Optical Pulses in Nonlinear Planar Waveguides — Pulse Compression and Soliton-Like Solutions." In Soliton-driven Photonics. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0682-8_27.

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Panigrahi, Prasanta K., and C. Nagaraja Kumar. "Soliton Solutions of the σ-Model and Disoriented Chiral Condensates." In Solitons. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1254-6_22.

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Pempinelli, F., M. Boiti, L. Martina, O. K. Pashaev, and D. Perrone. "New Soliton Solutions for the Davey-Stewartson Equation." In Solitons and Chaos. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-84570-3_41.

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Conference papers on the topic "Soliton solutions"

1

Evangel ides, S. G., L. F. Mollenauer, and J. P. Gordon. "Polarization multiplexing with solutions." In OSA Annual Meeting. Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.mrr3.

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We have examined, through numerical simulations, experiment, and analytic theory, the behavior of the polarization state of a stream of solitons in a long distance, all-optical transmission system consisting of spans of dispersion shifted fiber having a small (~0.2 ps/km1/2 randomly varying birefringence and periodically spaced erbium-doped fiber amplifiers. From the theory and simulations we find that a stream of solitons, all launched into such a system in the same polarization state, will emerge with all the solitons approximately in a common, well defined, polarization state. The pulse-to-

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2

Shipulin, A. V., D. G. Fursa, E. A. Golovchenko, and E. M. Dianov. "High repetition rate CW dark soliton train generation in a fiber with decreasing dispersion." In Nonlinear Guided-Wave Phenomena. Optica Publishing Group, 1993. http://dx.doi.org/10.1364/nlgwp.1993.tub.9.

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The non-linear Schrodinger equation (NLS) predicts an existence of stable solutions (e.g. solutions conserving amplitude and phase under propagation) for both positive and negative Group Velocity Dispersion (GVD) regions. The solution existing in the positive GVD region consist of a rapid dip in a CW background and is called a "dark soliton" analogously to a "bright soliton" for the negative GVD region [1,2]. The fundamental dark soliton is an anti- symmetric function of time, with an abrupt π phase shift and zero intensity at its center. Although the existence of dark optical solitons in fibe

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3

Yesmakhanova, Kuralay, Gaukhar Shaikhova, and Guldana Bekova. "Soliton solutions of the Hirota’s system." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959761.

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Afanasjev, V. V., E. M. Dianov, and V. N. Serkin. "Problem of Noise Evolution in Nonlinear Fiber Systems Based on Optical Soliton Effects." In Nonlinear Guided-Wave Phenomena. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/nlgwp.1989.thb4.

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Progress in the experiments with optical solitons, creation of new types of lasers-soliton lasers, developing of the "soliton" fiber systems for the data storage and transmission gave rise to a number of new problems in the soliton theory. One of such new problems directly connected with the experiment is the analysis of statistical solutions for the nonlinear equations describing processes of optical soliton formation in fibers. In this paper we present the results on the statistical modelling of the nonlinear dynamics of optical solitons and optical noise in the fiber systems for the data st

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Afanasjev, V. V., and V. N. Serkin. "Interaction of vector solitons." In Nonlinear Guided-Wave Phenomena. Optica Publishing Group, 1993. http://dx.doi.org/10.1364/nlgwp.1993.tub.13.

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Active interest is taken in polarization and two-wavelength phenomena in soliton propagation. Among intriguing experimental results are the polarization multiplexing [1], soliton logic [2], polarization intensity discrimination [3], polarization mode-locking [4,5], bound state of dark and bright optical solitons [6]. All these effects may be describes (at least qualitatively) by the vector Nonlinear Schrödinger equation (NLS) (1). This equation has a rich variety of solutions, and a lot of stationary (soliton) solutions were found by different analytical approaches (see [7] and references ther

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Weiner, A. M., J. P. Heritage, R. N. Thurston, et al. "Experimental studies of dark soliton propagation in fibers." In OSA Annual Meeting. Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.mbb1.

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Solitons are intense ultrashort pulses which propagate without distortion in optical fibers. Bright solitons, which exist for negative group velocity dispersion (GVD), have been investigated extensively over the past decade. Dark solitons, which consist of a short hole superimposed on a broad background pulse and which occur for positive GVD, have been studied much less, in part due to the lack of a convenient technique for producing the required specially shaped input dark pulses. We have developed a technique for precise synthesis of femtosecond optical waveforms, and we apply this technique

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Guner, Ozkan, Omer Unsal, Ahmet Bekir, and Abdelouahab Kadem. "Soliton solution and other solutions to a nonlinear fractional differential equation." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972761.

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Chakravarty, Sarbarish, Yuji Kodama, Wen Xiu Ma, Xing-biao Hu, and Qingping Liu. "Line-soliton solutions of the KP equation." In NONLINEAR AND MODERN MATHEMATICAL PHYSICS: Proceedings of the First International Workshop. AIP, 2010. http://dx.doi.org/10.1063/1.3367073.

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DE MARTINO, S., and G. LAURO. "SOLITON-LIKE SOLUTIONS FOR A CAPILLARY FLUID." In Proceedings of the 12th Conference on WASCOM 2003. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702937_0019.

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Torner, Lluis, Dumitru Mazilu, and Dumitru Mihalache. "Walking Spatial Solitons in Nonlinear Quadratic Media." In Nonlinear Guided Waves and Their Applications. Optica Publishing Group, 1996. http://dx.doi.org/10.1364/nlgw.1996.fd.2.

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Both, spatial and temporal solitons (more properly, solitary waves) exist in bulk crystals and in optical waveguides made of nonlinear quadratic media [1]-[3]. Bright spatial solitons have been already observed in second harmonic generation experiments [4]-[5]. Families of stationary soliton solutions of the governing are known to exist under ideal conditions, namely when there is no walk-off betwen the interacting waves [2]-[3]. Temporal walk-off is due to different group velocities of the waves forming the soliton, while spatial beam walk-off is due to different propagation directions of ene

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Reports on the topic "Soliton solutions"

1

Gerdjikov, Vladimir S. How Many Types of Soliton Solutions Do We Know? GIQ, 2012. http://dx.doi.org/10.7546/giq-7-2006-11-34.

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Babalic, Corina N., Radu Constantinescu, and Vladimir S. Gerdjikov. On the Soliton Solutions of a Family of Tzitzeica Equations. Jgsp, 2015. http://dx.doi.org/10.7546/jgsp-37-2015-1-24.

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Grahovski, Georgi G., and Vladimir S. Gerdjikov. On the Multi-Component NLS Type Equations on Symmetric Spaces: Reductions and Soliton Solutions. GIQ, 2012. http://dx.doi.org/10.7546/giq-6-2005-203-217.

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Chen, P. Brane Inflation, Solitons and Cosmological Solutions: I. Office of Scientific and Technical Information (OSTI), 2005. http://dx.doi.org/10.2172/839660.

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