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Cosine effect in ocean models
On the transverse instability of one dimensional capillary-gravity waves
1. | IRMAR, Université de Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France |
2. | Département de Mathématiques, Université Lille I, 59 655 Villeneuve d’Ascq Cedex, France |
[1] |
Xingxing Liu. Stability in the energy space of the sum of $ N $ solitary waves for an equation modelling shallow water waves of moderate amplitude. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022105 |
[2] |
H. Kalisch. Stability of solitary waves for a nonlinearly dispersive equation. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 709-717. doi: 10.3934/dcds.2004.10.709 |
[3] |
Kristoffer Varholm. Solitary gravity-capillary water waves with point vortices. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3927-3959. doi: 10.3934/dcds.2016.36.3927 |
[4] |
Angel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, Javier Gómez-Serrano. Structural stability for the splash singularities of the water waves problem. Discrete and Continuous Dynamical Systems, 2014, 34 (12) : 4997-5043. doi: 10.3934/dcds.2014.34.4997 |
[5] |
Santosh Bhattarai. Stability of normalized solitary waves for three coupled nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 1789-1811. doi: 10.3934/dcds.2016.36.1789 |
[6] |
Steve Levandosky, Yue Liu. Stability and weak rotation limit of solitary waves of the Ostrovsky equation. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 793-806. doi: 10.3934/dcdsb.2007.7.793 |
[7] |
Amjad Khan, Dmitry E. Pelinovsky. Long-time stability of small FPU solitary waves. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2065-2075. doi: 10.3934/dcds.2017088 |
[8] |
Khaled El Dika. Asymptotic stability of solitary waves for the Benjamin-Bona-Mahony equation. Discrete and Continuous Dynamical Systems, 2005, 13 (3) : 583-622. doi: 10.3934/dcds.2005.13.583 |
[9] |
Sevdzhan Hakkaev. Orbital stability of solitary waves of the Schrödinger-Boussinesq equation. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1043-1050. doi: 10.3934/cpaa.2007.6.1043 |
[10] |
Elena Kartashova. Nonlinear resonances of water waves. Discrete and Continuous Dynamical Systems - B, 2009, 12 (3) : 607-621. doi: 10.3934/dcdsb.2009.12.607 |
[11] |
Robert McOwen, Peter Topalov. Asymptotics in shallow water waves. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3103-3131. doi: 10.3934/dcds.2015.35.3103 |
[12] |
Thomas Y. Hou, Pingwen Zhang. Convergence of a boundary integral method for 3-D water waves. Discrete and Continuous Dynamical Systems - B, 2002, 2 (1) : 1-34. doi: 10.3934/dcdsb.2002.2.1 |
[13] |
José Raúl Quintero, Juan Carlos Muñoz Grajales. Solitary waves for an internal wave model. Discrete and Continuous Dynamical Systems, 2016, 36 (10) : 5721-5741. doi: 10.3934/dcds.2016051 |
[14] |
Jerry Bona, Hongqiu Chen. Solitary waves in nonlinear dispersive systems. Discrete and Continuous Dynamical Systems - B, 2002, 2 (3) : 313-378. doi: 10.3934/dcdsb.2002.2.313 |
[15] |
Orlando Lopes. A linearized instability result for solitary waves. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 115-119. doi: 10.3934/dcds.2002.8.115 |
[16] |
R. S. Johnson. A selection of nonlinear problems in water waves, analysed by perturbation-parameter techniques. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1497-1522. doi: 10.3934/cpaa.2012.11.1497 |
[17] |
Harunori Monobe, Hirokazu Ninomiya. Multiple existence of traveling waves of a free boundary problem describing cell motility. Discrete and Continuous Dynamical Systems - B, 2014, 19 (3) : 789-799. doi: 10.3934/dcdsb.2014.19.789 |
[18] |
Walter A. Strauss. Vorticity jumps in steady water waves. Discrete and Continuous Dynamical Systems - B, 2012, 17 (4) : 1101-1112. doi: 10.3934/dcdsb.2012.17.1101 |
[19] |
Jerry L. Bona, Henrik Kalisch. Models for internal waves in deep water. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 1-20. doi: 10.3934/dcds.2000.6.1 |
[20] |
Vera Mikyoung Hur. On the formation of singularities for surface water waves. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1465-1474. doi: 10.3934/cpaa.2012.11.1465 |
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