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Journal articles on the topic 'Solitary waves'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Chu, Jen-Ping, Patrick Lynett, and Mitul Luhar. "EXPERIMENTAL STUDY OF INTERNAL SOLITARY WAVES INTERACTION WITH SURFACE SOLITARY WAVES." Coastal Engineering Proceedings, no. 38 (May 29, 2025): 40. https://doi.org/10.9753/icce.v38.waves.40.

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Internal solitary waves (ISWs) consist of a non-periodic single-crest profile resulting from the balance between non-linearity and dispersion. They can be a significant source of momentum transport in any stratified systems, such as oceans and estuaries. Previous experiments have primarily utilized lock- release mechanisms to generate internal solitary waves in two-layer systems. This provides limited control over wave properties and limits its studies with barotropic wave interactions. The present effort attempts to validate the performance of a new wave generation method, termed the Jet Arra

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2

Fitzgerald, Richard J. "Interacting solitary waves." Physics Today 65, no. 11 (2012): 20. http://dx.doi.org/10.1063/pt.3.1777.

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3

Ignatov, A. M. "Magnetosonic Solitary Waves." Plasma Physics Reports 50, no. 5 (2024): 603–10. http://dx.doi.org/10.1134/s1063780x24600555.

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Abstract The set of equations is obtained that describes the nonlinear three-dimensional dynamics of magnetosonic waves. Plane solitary waves propagating at a small angle to the guiding magnetic field have been studied. Three-dimensional spatially localized waves have been qualitatively studied.

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4

Ignatov, A. M. "Magnetosonic solitary waves." Fizika plazmy 50, no. 5 (2024): 579–87. https://doi.org/10.31857/s0367292124050075.

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The set of equations is obtained that describes the nonlinear three-dimensional dynamics of magnetosonic waves. Plane solitary waves propagating at a small angle to the guiding magnetic field have been studied. Three-dimensional spatially localized waves have been qualitatively studied.

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5

Weidman, P. D., and R. Zakhem. "Cylindrical solitary waves." Journal of Fluid Mechanics 191, no. -1 (1988): 557. http://dx.doi.org/10.1017/s0022112088001703.

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6

Mason, Joanne, and Edgar Knobloch. "Solitary dynamo waves." Physics Letters A 355, no. 2 (2006): 110–17. http://dx.doi.org/10.1016/j.physleta.2006.02.013.

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7

Qureshi, M. N. S., Jian Kui Shi, and H. A. Shah. "Electrostatic Solitary Waves." Journal of Fusion Energy 31, no. 2 (2011): 112–17. http://dx.doi.org/10.1007/s10894-011-9439-7.

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8

Chen, X. N., and W. Maschek. "Nuclear solitary waves." PAMM 8, no. 1 (2008): 10489–90. http://dx.doi.org/10.1002/pamm.200810489.

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9

Weidman, P. D., and M. G. Velarde. "Internal Solitary Waves." Studies in Applied Mathematics 86, no. 2 (1992): 167–84. http://dx.doi.org/10.1002/sapm1992862167.

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10

Lo, Peter H. Y., Wen-Yu Chen, and Chun-Jui Huang. "LABORATORY EXPERIMENTS ON THE RUNUP OF LEADING-DEPRESSION N-WAVES." Coastal Engineering Proceedings, no. 38 (May 29, 2025): 14. https://doi.org/10.9753/icce.v38.waves.14.

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Real tsunamis often lead with a depression wave, causing coastal water level to lower before the main tsunami wave arrives and floods the coast. The widely used benchmark wave, the solitary wave, cannot capture this phenomenon, in addition to the many drawbacks in using the solitary wave as a model tsunami wave form (Madsen et al. 2008). Although alternative tsunami wave forms have been proposed to capture the water level withdrawal phenomenon, in particular the leading- depression N-waves (LDN), a consistent method for generating and characterizing LDNs had been lacking. In this study we adop

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11

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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12

Lubin, Pierre, and Stéphane Glockner. "NUMERICAL SIMULATIONS OF BREAKING SOLITARY WAVES." Coastal Engineering Proceedings 1, no. 33 (2012): 59. http://dx.doi.org/10.9753/icce.v33.waves.59.

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This paper presents the application of a parallel numerical code to breaking solitary waves impacting a seawall structure. The three-dimensional Navier-Stokes equations are solved in air and water, coupled with a subgrid-scale model to take turbulence into account. We compared three numerical methods for the free-surface description, using the classical VOF-PLIC and VOF-TVD methods, and an original VOF-SM method recently developed in our numerical tool (Vincent et al., 2010). Some experimental data for solitary waves impinging and overtopping coastal structures are available in literature (Hsi

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13

LAMB, KEVIN G. "A numerical investigation of solitary internal waves with trapped cores formed via shoaling." Journal of Fluid Mechanics 451 (January 25, 2002): 109–44. http://dx.doi.org/10.1017/s002211200100636x.

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The formation of solitary internal waves with trapped cores via shoaling is investigated numerically. For density fields for which the buoyancy frequency increases monotonically towards the surface, sufficiently large solitary waves break as they shoal and form solitary-like waves with trapped fluid cores. Properties of large-amplitude waves are shown to be sensitive to the near-surface stratification. For the monotonic stratifications considered, waves with open streamlines are limited in amplitude by the breaking limit (maximum horizontal velocity equals wave propagation speed). When an expo

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14

Moe, Sandar Nyunt. "Shallow Water Waves, Solitary Waves and Ocean Waves." Dagon University Research Journal Vol.6, no. 2014 (2019): Pg.189–200. https://doi.org/10.5281/zenodo.3547200.

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In this paper, we study about properties and natures of water waves. Firstly, types of waves, classification of waves and basic properties of waves are presented. Then, we’ll talk about solitary waves and show their beautiful phenomenon by mathematically. We construct asymptotic solutions for multi-soliton solutions, using the inverse scattering transform method. Moreover, we study about three types of waves in the ocean such as wind-driver waves, tides and tsunami with their natures and properties.  

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15

Wang, Yufei, and Philip Li-Fan Liu. "DAMPING OF FINITE AMPLITUDE SOLITARY WAVES IN A FLUME." Coastal Engineering Proceedings, no. 37 (September 1, 2023): 7. http://dx.doi.org/10.9753/icce.v37.waves.7.

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Solitary wave is a permanent wave when the dissipation is ignored. Many analytical solutions have been developed for finite amplitude solitary waves. In additional to the perturbation solutions, closed form solutions are also available (e.g., McCowan 1891, Clamond and Fructus 2003, being denoted as CF from hereon), which are more accuracy, especially for larger amplitude solitary waves which were discussed in Wang and Liu (2022). In Wang and Liu (2022) ’s laboratory experiments, solitary waves are slowly damped along the wave flume, which can be attributed to the energy dissipation inside the

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16

BAKHOLDIN, I., A. IL'ICHEV, and A. ZHARKOV. "Steady magnetoacoustic waves and decay of solitonic structures in a finite-beta plasma." Journal of Plasma Physics 67, no. 1 (2002): 1–26. http://dx.doi.org/10.1017/s0022377801001337.

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The solitonic, periodic and quasiperiodic solutions that obey the full system of transport equations describing one-dimensional motion of a isotropic collisionless quasineutral plasma in a magnetic field are treated. The domains of physical parameters of such a plasma are determined for fast and slow magnetoacoustic branches, where solitary waves and generalized solitary waves exist. In the parameter domain where solitary waves are replaced by non-local generalized solitary waves, the localized disturbances are subject to decay, which has qualitatively different mechanisms for fast and slow ma

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17

Yu, Wen, Fenggang Wang, Jianguo Lin, and Dong Li. "Numerical Simulation of the Force Acting on the Riser by Two Internal Solitary Waves." Applied Sciences 12, no. 10 (2022): 4873. http://dx.doi.org/10.3390/app12104873.

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An internal wave is a typical dynamic process. As an internal wave, an internal solitary wave usually occurs between two layers of fluids with different densities. Compared with general internal waves, internal solitary waves have large amplitudes, fast propagation speeds, short-wave periods, and often have tremendous energy. The propagation causes strong convergence and divergence of seawater and generates a sudden strong current. Due to its various characteristics, the propagation of internal solitary waves can cause serious harm to offshore engineering structures. Therefore, studying the ef

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18

Baldock, T. E., D. Peiris, and A. J. Hogg. "Overtopping of solitary waves and solitary bores on a plane beach." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2147 (2012): 3494–516. http://dx.doi.org/10.1098/rspa.2011.0729.

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The overtopping of solitary waves and bores present major hazards during the initial phase of tsunami inundation and storm surges. This paper presents new laboratory data on overtopping events by both solitary waves and solitary bores. Existing empirical overtopping scaling laws are found to be deficient for these wave forms. Two distinct scaling regimes are instead identified. For solitary waves, the overtopping rates scale linearly with the deficit in run-up freeboard. The volume flux in the incident solitary wave is also an important parameter, and a weak dependence on the nonlinearity of t

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19

Kapitula, Todd. "Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 3 (1998): 585–629. http://dx.doi.org/10.1017/s030821050002165x.

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The existence of bright and dark multi-bump solitary waves for Ginzburg–Landau type perturbations of the cubic-quintic Schrodinger equation is considered. The waves in question are not perturbations of known analytic solitary waves, but instead arise as a bifurcation from a heteroclinic cycle in a three-dimensional ODE phase space. Using geometric singular perturbation techniques, regions in parameter space for which 1-bump bright and dark solitary waves will bifurcate are identified. The existence of N-bump dark solitary waves (N ≧ 1) is shown via an application of the Exchange Lemma with Exp

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20

Shen, Yuan, Bo Tian, Chong-Dong Cheng, and Tian-Yu Zhou. "Pfaffian solutions and nonlinear waves of a (3 + 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics." Physics of Fluids 35, no. 2 (2023): 025103. http://dx.doi.org/10.1063/5.0135174.

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Fluid mechanics is concerned with the behavior of liquids and gases at rest or in motion, where the nonlinear waves and their interactions are important. Hereby, we study a (3 + 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics. We determine a bilinear form of that system via the Hirota method. Nth-order Pfaffian solutions are obtained via the Pfaffian technique and our bilinear form, where N is a positive integer. Based on the Nth-order Pfaffian solutions, we derive the N-soliton, higher-order breather, and hybrid solutions. Using those solutions, w

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21

Nakamura, Y., and K. Ohtani. "Solitary waves in an ion-beam-plasma system." Journal of Plasma Physics 53, no. 2 (1995): 235–43. http://dx.doi.org/10.1017/s0022377800018146.

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Solitary waves in an ion-beam-plasma system are investigated theoretically using the pseudo-potential method, including finite temperatures of plasma ions and beam ions. The beam velocity is high enough to avoid ion-ion instability. Three kinds of solitary waves are possible, corresponding to ion- acoustic waves and to fast and slow space-charge waves in the beam. To observe the formation of solitary waves from an initial positive pulse, numerical simulations are performed. For the slow beam mode, a smaller solitary wave appears at the leading part of the pulse, which is a result of negative n

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22

Xu, Chengzhu, and Marek Stastna. "On the interaction of short linear internal waves with internal solitary waves." Nonlinear Processes in Geophysics 25, no. 1 (2018): 1–17. http://dx.doi.org/10.5194/npg-25-1-2018.

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Abstract. We study the interaction of small-scale internal wave packets with a large-scale internal solitary wave using high-resolution direct numerical simulations in two dimensions. A key finding is that for wave packets whose constituent waves are short in comparison to the solitary wave width, the interaction leads to an almost complete destruction of the short waves. For mode-1 short waves in the packet, as the wavelength increases, a cutoff is reached, and for larger wavelengths the waves in the packet are able to maintain their structure after the interaction. This cutoff corresponds to

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23

Nakayama, Keisuke, Taro Kakinuma, Hidekazu Tsuji, and Masayuki Oikawa. "NONLINEAR OBLIQUE INTERACTION OF LARGE AMPLITUDE INTERNAL SOLITARY WAVES." Coastal Engineering Proceedings 1, no. 33 (2012): 19. http://dx.doi.org/10.9753/icce.v33.waves.19.

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Solitary waves are typical nonlinear long waves in the ocean. The two-dimensional interaction of solitary waves has been shown to be essentially different from the one-dimensional case and can be related to generation of large amplitude waves (including ‘freak waves’). Concerning surface-water waves, Miles (1977) theoretically analyzed interaction of three solitary waves, which is called “resonant interaction” because of the relation among parameters of each wave. Weakly-nonlinear numerical study (Funakoshi, 1980) and fully-nonlinear one (Tanaka, 1993) both clarified the formation of large amp

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24

CHAMPNEYS, ALAN R., and MARK D. GROVES. "A global investigation of solitary-wave solutions to a two-parameter model for water waves." Journal of Fluid Mechanics 342 (July 10, 1997): 199–229. http://dx.doi.org/10.1017/s0022112097005193.

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The model equationformula herearises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravity–capillary water waves. Being Hamiltonian, reversible and depending upon two parameters, it shares the structure of the full steady water-wave problem. Moreover, all known analytical results for local bifurcations of solitary-wave solutions to the full water-wave problem have precise counterparts for the model equation.At the time of writing two major open problems for steady water waves are attracting particular attention. The first concerns the possible existence of

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25

Wang, Zhan, Emilian I. Părău, Paul A. Milewski, and Jean-Marc Vanden-Broeck. "Numerical study of interfacial solitary waves propagating under an elastic sheet." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2168 (2014): 20140111. http://dx.doi.org/10.1098/rspa.2014.0111.

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Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches

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26

Kenyon, Kern E. "Stability of Solitary Waves." Physics Essays 14, no. 3 (2001): 266–69. http://dx.doi.org/10.4006/1.3025492.

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27

Chen, Yijiang, and Javid Atai. "Parametric spatial solitary waves." Optics Letters 19, no. 17 (1994): 1287. http://dx.doi.org/10.1364/ol.19.001287.

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28

Craig, Walter, and Peter Sternberg. "Symmetry of solitary waves." Communications in Partial Differential Equations 13, no. 5 (1988): 603–33. http://dx.doi.org/10.1080/03605308808820554.

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29

Stoychev, K. T., M. T. Primatarowa, and K. Marinov. "Exciton-polariton solitary waves." European Physical Journal B - Condensed Matter 29, no. 2 (2002): 301–4. http://dx.doi.org/10.1140/epjb/e2002-00305-8.

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30

Părău, Emilian I. "Solitary interfacial hydroelastic waves." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2111 (2017): 20170099. http://dx.doi.org/10.1098/rsta.2017.0099.

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Solitary waves travelling along an elastic plate present between two fluids with different densities are computed in this paper. Different two-dimensional configurations are considered: the upper fluid can be of infinite extent, bounded by a rigid wall or under a second elastic plate. The dispersion relation is obtained for each case and numerical codes based on integro-differential formulations for the full nonlinear problem are derived. This article is part of the theme issue ‘Nonlinear water waves’.

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31

Puerta, J., and P. Martin. "Bi-dust solitary waves." Journal of Physics: Conference Series 370 (June 19, 2012): 012042. http://dx.doi.org/10.1088/1742-6596/370/1/012042.

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32

Vanden-Broeck, J. M., and Joseph B. Keller. "Surfing on solitary waves." Journal of Fluid Mechanics 198, no. -1 (1989): 115. http://dx.doi.org/10.1017/s0022112089000066.

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33

Poladian, L., A. W. Snyder, and D. J. Mitchell. "Low-interaction solitary waves." Optics Communications 91, no. 1-2 (1992): 97–98. http://dx.doi.org/10.1016/0030-4018(92)90108-4.

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34

Guoxiang, Huang, Lou Senyue, and Dai Xianxi. "Cylindrical envelope solitary waves." Chinese Physics Letters 7, no. 9 (1990): 398–401. http://dx.doi.org/10.1088/0256-307x/7/9/005.

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35

Lanzano, Paolo. "Solitary waves of vortices." Earth, Moon, and Planets 69, no. 3 (1995): 271–83. http://dx.doi.org/10.1007/bf00643788.

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36

Sutherland, B. R., K. J. Barrett, and G. N. Ivey. "Shoaling internal solitary waves." Journal of Geophysical Research: Oceans 118, no. 9 (2013): 4111–24. http://dx.doi.org/10.1002/jgrc.20291.

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37

Ryskin, Nikita. "Solitary space-charge waves." Izvestiya VUZ. Applied Nonlinear Dynamics 2, no. 3 (1994): 84–92. https://doi.org/10.18500/0869-6632-1994-2-5-84-92.

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Solitary space-charge waves on a cylindrical electron beam, moving in a metal waveguide are studied. The beam is assumed to be charge-neutralized and focused by a strong external magnetic field. Exact solitary wave solutions in an implicit form are obtained and their breaking conditions are determined. Processes of solitary waves ехitation and interaction are examined numerically. Overtaking collisions, in which the waves travel in the same direction when viewed from the beam frame (i.e., collisions of two fast or two slow waves), are found to be almost elastic. On the other hand, the «head-on

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38

Khaled, Mahmood A. H., Ibrahim G. H. Loqman, and Kauther I. Alkuhlani. "PROPAGATION OF ION ACOUSTIC WAVES IN A MAGNETIZED QUANTUM PLASMA IN THE PRESENCE OF EXCHANGE-CORRELATION EFFECTS." Electronic Journal of University of Aden for Basic and Applied Sciences 3, no. 2 (2022): 84–92. http://dx.doi.org/10.47372/ejua-ba.2022.2.156.

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The nonlinear propagation of ion acoustic solitary waves are studied in a magnetized quantum plasma consisting of cold inertia ions and inertialless quantum electrons and positrons, including exchange-correlation effects., A Zakharov-Kuznetsov equation is derived by using the reductive perturbation method. The effects of quantum plasma parameters on the propagation characteristics of the ion acoustic solitary waves have been investigated. It is found that the phase velocity, amplitude and width of the solitary waves are significantly affected by the presence of exchange-correlation potentials

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39

LIU, ZHENGRONG, and JIBIN LI. "BIFURCATIONS OF SOLITARY WAVES AND DOMAIN WALL WAVES FOR KdV-LIKE EQUATION WITH HIGHER ORDER NONLINEARITY." International Journal of Bifurcation and Chaos 12, no. 02 (2002): 397–407. http://dx.doi.org/10.1142/s0218127402004425.

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Bifurcations of solitary waves and domain wall waves for a KdV-like equation with higher order nonlinearity are studied, by using bifurcation theory of planar dynamical systems. Bifurcation parameter sets are shown. Numbers of solitary waves and domain wall waves are given. Under some parameter conditions, a lot of explicit formulas of solitary wave solutions and domain wall solutions are obtained.

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40

Gavrilov, N., V. Liapidevskii, and K. Gavrilova. "Mass and momentum transfer by solitary internal waves in a shelf zone." Nonlinear Processes in Geophysics 19, no. 2 (2012): 265–72. http://dx.doi.org/10.5194/npg-19-265-2012.

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Abstract. The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the "swash" zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of solitary waves symmetric with respect to the unperturbed interface is constructed. It is shown that, taking into account the friction on interfaces in the mathematical model, it is possible to describe adequately the change in the phase and

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41

Pickett, J. S., L. J. Chen, S. W. Kahler, et al. "On the generation of solitary waves observed by Cluster in the near-Earth magnetosheath." Nonlinear Processes in Geophysics 12, no. 2 (2005): 181–93. http://dx.doi.org/10.5194/npg-12-181-2005.

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Abstract. Through case studies involving Cluster waveform observations, solitary waves in the form of bipolar and tripolar pulses have recently been found to be quite abundant in the near-Earth dayside magnetosheath. We expand on the results of those previous studies by examining the distribution of solitary waves from the bow shock to the magnetopause using Cluster waveform data. Cluster's orbit allows for the measurement of solitary waves in the magnetosheath from about 10 RE to 19.5 RE. Our results clearly show that within the magnetosheath, solitary waves are likely to be observed at any d

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42

Wu, Yun, and Zhengrong Liu. "Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation." Advances in Mathematical Physics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/812120.

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We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equationut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the sym

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43

Su, Chau-Hsing, and Qi-su Zou. "Waves generated by collisions of solitary waves." Physical Review A 35, no. 11 (1987): 4738–42. http://dx.doi.org/10.1103/physreva.35.4738.

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44

LIU, RUI, and WEIFANG YAN. "SOME COMMON EXPRESSIONS AND NEW BIFURCATION PHENOMENA FOR NONLINEAR WAVES IN A GENERALIZED mKdV EQUATION." International Journal of Bifurcation and Chaos 23, no. 03 (2013): 1330007. http://dx.doi.org/10.1142/s0218127413300073.

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Using the bifurcation method of dynamical systems, we study nonlinear waves in the generalized mKdV equation ut + a(1 + bu2)u2ux + uxxx = 0. (i) We obtain four types of new expressions. The first type is composed of four common expressions of the symmetric solitary waves, the kink waves and the blow-up waves. The second type includes four common expressions of the anti-symmetric solitary waves, the kink waves and the blow-up waves. The third type is made of two trigonometric expressions of periodic-blow-up waves. The fourth type is composed of two fractional expressions of 1-blow-up waves. (ii

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45

Zhang, Weiguo, Xu Chen, Zhengming Li, and Haiyan Zhang. "Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms." Journal of Applied Mathematics 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/963987.

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This paper investigates the orbital stability of solitary waves for the generalized symmetric regularized-long-wave equations with two nonlinear terms and analyzes the influence of the interaction between two nonlinear terms on the orbital stability. SinceJis not onto, Grillakis-Shatah-Strauss theory cannot be applied on the system directly. We overcome this difficulty and obtain the general conclusion on orbital stability of solitary waves in this paper. Then, according to two exact solitary waves of the equations, we deduce the explicit expression of discriminationd′′(c)and give several suff

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46

LAMB, KEVIN G. "Shoaling solitary internal waves: on a criterion for the formation of waves with trapped cores." Journal of Fluid Mechanics 478 (March 10, 2003): 81–100. http://dx.doi.org/10.1017/s0022112002003269.

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Shoaling solitary internal waves are ubiquitous features in the coastal regions of the world's oceans where waves with a core of recirculating fluid (trapped cores) can provide an effective transport mechanism. Here, numerical evidence is presented which suggests that there is a close connection between the limiting behaviour of large-amplitude solitary waves and the formation of such waves via shoaling. For some background states, large-amplitude waves are broad, having a nearly horizontal flow in their centre. The flow in the centre of such waves is called a conjugate flow. For other backgro

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47

LAGET, O., and F. DIAS. "Numerical computation of capillary–gravity interfacial solitary waves." Journal of Fluid Mechanics 349 (October 25, 1997): 221–51. http://dx.doi.org/10.1017/s0022112097006861.

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Two types of capillary–gravity interfacial solitary waves are computed numerically: ‘classical’ solitary waves which bifurcate from a uniform flow at a critical value of the velocity and solitary waves in the form of wave packets which bifurcate from a train of infinitesimal periodic waves with equal phase and group velocities. The effects of finite amplitude are shown to be quite different from the pure gravity case for the classical solitary waves. The solitary waves in the form of wave packets, which are known to exist for small density ratios, are shown to exist even for larger density rat

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48

YANG, T. S., and T. R. AKYLAS. "On asymmetric gravity–capillary solitary waves." Journal of Fluid Mechanics 330 (January 10, 1997): 215–32. http://dx.doi.org/10.1017/s0022112096003643.

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Symme tric gravity–capillary solitary waves with decaying oscillatory tails are known to bifurcate from infinitesimal periodic waves at the minimum value of the phase speed where the group velocity is equal to the phase speed. In the small-amplitude limit, these solitary waves may be interpreted as envelope solitons with stationary crests and are described by the nonlinear Schrödinger (NLS) equation to leading order. In line with this interpretation, it would appear that one may also co nstruct asymmetric solitary waves by shifting the carrier oscillations relative to the envelope of a symmetr

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49

Shi, Yunlong, Baoshu Yin, Hongwei Yang, Dezhou Yang, and Zhenhua Xu. "Dissipative Nonlinear Schrödinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/643652.

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We solve the so-called dissipative nonlinear Schrödinger equation by means of multiple scales analysis and perturbation method to describe envelope solitary Rossby waves with dissipation effect in stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency, andβeffect are important factors to form the envelope solitary Rossby waves. By employing trial function method, the asymptotic solution of dissipative nonlinear Schrödinger equation is derived. Based on the solution, the effect of dissipatio

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50

Wang, Zhan, and Paul A. Milewski. "Dynamics of gravity–capillary solitary waves in deep water." Journal of Fluid Mechanics 708 (August 15, 2012): 480–501. http://dx.doi.org/10.1017/jfm.2012.320.

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AbstractThe dynamics of solitary gravity–capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time-dependent solutions, we simplify the full potential flow problem by using surface variables and taking a particular cubic truncation possessing a Hamiltonian with desirable properties. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of solitary waves for a two-dimensional fluid domain, and with higher-order truncations in three

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