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Two-pulse solutions in the fifth-order KdV equation: Rigorous theory and numerical approximations
1. | Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada, Canada |
[1] |
Juan-Ming Yuan, Jiahong Wu. A dual-Petrov-Galerkin method for two integrable fifth-order KdV type equations. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1525-1536. doi: 10.3934/dcds.2010.26.1525 |
[2] |
Yingte Sun, Xiaoping Yuan. Quasi-periodic solution of quasi-linear fifth-order KdV equation. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : 6241-6285. doi: 10.3934/dcds.2018268 |
[3] |
Jibin Li, Yi Zhang. Exact solitary wave and quasi-periodic wave solutions for four fifth-order nonlinear wave equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 623-631. doi: 10.3934/dcdsb.2010.13.623 |
[4] |
Márcio Cavalcante, Chulkwang Kwak. Local well-posedness of the fifth-order KdV-type equations on the half-line. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2607-2661. doi: 10.3934/cpaa.2019117 |
[5] |
Pedro Isaza, Juan López, Jorge Mejía. Cauchy problem for the fifth order Kadomtsev-Petviashvili (KPII) equation. Communications on Pure and Applied Analysis, 2006, 5 (4) : 887-905. doi: 10.3934/cpaa.2006.5.887 |
[6] |
Netra Khanal, Ramjee Sharma, Jiahong Wu, Juan-Ming Yuan. A dual-Petrov-Galerkin method for extended fifth-order Korteweg-de Vries type equations. Conference Publications, 2009, 2009 (Special) : 442-450. doi: 10.3934/proc.2009.2009.442 |
[7] |
Willem M. Schouten-Straatman, Hermen Jan Hupkes. Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 5017-5083. doi: 10.3934/dcds.2019205 |
[8] |
Zhaosheng Feng, Qingguo Meng. Exact solution for a two-dimensional KDV-Burgers-type equation with nonlinear terms of any order. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 285-291. doi: 10.3934/dcdsb.2007.7.285 |
[9] |
Jundong Wang, Lijun Zhang, Elena Shchepakina, Vladimir Sobolev. Solitary waves of singularly perturbed generalized KdV equation with high order nonlinearity. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022124 |
[10] |
Jun-ichi Segata. Initial value problem for the fourth order nonlinear Schrödinger type equation on torus and orbital stability of standing waves. Communications on Pure and Applied Analysis, 2015, 14 (3) : 843-859. doi: 10.3934/cpaa.2015.14.843 |
[11] |
Gianne Derks, Sara Maad, Björn Sandstede. Perturbations of embedded eigenvalues for the bilaplacian on a cylinder. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 801-821. doi: 10.3934/dcds.2008.21.801 |
[12] |
Jerry L. Bona, Angel Durán, Dimitrios Mitsotakis. Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. approximations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 87-111. doi: 10.3934/dcds.2020215 |
[13] |
Giuseppe Maria Coclite, Lorenzo di Ruvo. Discontinuous solutions for the generalized short pulse equation. Evolution Equations and Control Theory, 2019, 8 (4) : 737-753. doi: 10.3934/eect.2019036 |
[14] |
Anwar Ja'afar Mohamad Jawad, Mohammad Mirzazadeh, Anjan Biswas. Dynamics of shallow water waves with Gardner-Kadomtsev-Petviashvili equation. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1155-1164. doi: 10.3934/dcdss.2015.8.1155 |
[15] |
Xiaoxiao Zheng, Hui Wu. Orbital stability of periodic traveling wave solutions to the coupled compound KdV and MKdV equations with two components. Mathematical Foundations of Computing, 2020, 3 (1) : 11-24. doi: 10.3934/mfc.2020002 |
[16] |
Changchun Liu, Zhao Wang. Time periodic solutions for a sixth order nonlinear parabolic equation in two space dimensions. Communications on Pure and Applied Analysis, 2014, 13 (3) : 1087-1104. doi: 10.3934/cpaa.2014.13.1087 |
[17] |
Mamoru Okamoto. Asymptotic behavior of solutions to a higher-order KdV-type equation with critical nonlinearity. Evolution Equations and Control Theory, 2019, 8 (3) : 567-601. doi: 10.3934/eect.2019027 |
[18] |
S. Raynor, G. Staffilani. Low regularity stability of solitons for the KDV equation. Communications on Pure and Applied Analysis, 2003, 2 (3) : 277-296. doi: 10.3934/cpaa.2003.2.277 |
[19] |
Reika Fukuizumi. Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 525-544. doi: 10.3934/dcds.2001.7.525 |
[20] |
François Genoud. Existence and stability of high frequency standing waves for a nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1229-1247. doi: 10.3934/dcds.2009.25.1229 |
2020 Impact Factor: 1.327
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