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A dual-Petrov-Galerkin method for extended fifth-order Korteweg-de Vries type equations
1. | Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States, United States, United States |
[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] |
Marina Chugunova, Dmitry Pelinovsky. Two-pulse solutions in the fifth-order KdV equation: Rigorous theory and numerical approximations. Discrete and Continuous Dynamical Systems - B, 2007, 8 (4) : 773-800. doi: 10.3934/dcdsb.2007.8.773 |
[3] |
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 |
[4] |
Torsten Keßler, Sergej Rjasanow. Fully conservative spectral Galerkin–Petrov method for the inhomogeneous Boltzmann equation. Kinetic and Related Models, 2019, 12 (3) : 507-549. doi: 10.3934/krm.2019021 |
[5] |
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 |
[6] |
Jingwei Hu, Jie Shen, Yingwei Wang. A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions. Kinetic and Related Models, 2020, 13 (4) : 677-702. doi: 10.3934/krm.2020023 |
[7] |
Jie Shen, Li-Lian Wang. Laguerre and composite Legendre-Laguerre Dual-Petrov-Galerkin methods for third-order equations. Discrete and Continuous Dynamical Systems - B, 2006, 6 (6) : 1381-1402. doi: 10.3934/dcdsb.2006.6.1381 |
[8] |
Shan Li, Shi-Mi Yan, Zhong-Qing Wang. Efficient Legendre dual-Petrov-Galerkin methods for odd-order differential equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1543-1563. doi: 10.3934/dcdsb.2019239 |
[9] |
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 |
[10] |
Esther S. Daus, Shi Jin, Liu Liu. Spectral convergence of the stochastic galerkin approximation to the boltzmann equation with multiple scales and large random perturbation in the collision kernel. Kinetic and Related Models, 2019, 12 (4) : 909-922. doi: 10.3934/krm.2019034 |
[11] |
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 |
[12] |
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 |
[13] |
Jerry L. Bona, Didier Pilod. Stability of solitary-wave solutions to the Hirota-Satsuma equation. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1391-1413. doi: 10.3934/dcds.2010.27.1391 |
[14] |
Aiyong Chen, Chi Zhang, Wentao Huang. Limit speed of traveling wave solutions for the perturbed generalized KdV equation. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022048 |
[15] |
Hisashi Okamoto, Takashi Sakajo, Marcus Wunsch. Steady-states and traveling-wave solutions of the generalized Constantin--Lax--Majda equation. Discrete and Continuous Dynamical Systems, 2014, 34 (8) : 3155-3170. doi: 10.3934/dcds.2014.34.3155 |
[16] |
Na An, Chaobao Huang, Xijun Yu. Error analysis of discontinuous Galerkin method for the time fractional KdV equation with weak singularity solution. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 321-334. doi: 10.3934/dcdsb.2019185 |
[17] |
Út V. Lê. Contraction-Galerkin method for a semi-linear wave equation. Communications on Pure and Applied Analysis, 2010, 9 (1) : 141-160. doi: 10.3934/cpaa.2010.9.141 |
[18] |
Juan-Ming Yuan, Jiahong Wu. The complex KdV equation with or without dissipation. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 489-512. doi: 10.3934/dcdsb.2005.5.489 |
[19] |
Andrew Comech, Elena Kopylova. Orbital stability and spectral properties of solitary waves of Klein–Gordon equation with concentrated nonlinearity. Communications on Pure and Applied Analysis, 2021, 20 (6) : 2187-2209. doi: 10.3934/cpaa.2021063 |
[20] |
Jibin Li, Yan Zhou. Bifurcations and exact traveling wave solutions for the nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 3083-3097. doi: 10.3934/dcdss.2020113 |
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