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Forced oscillations of the Korteweg-de Vries equation on a bounded domain and their stability
A dual-Petrov-Galerkin method for two integrable fifth-order KdV type equations
1. | Department of Financial and Computational Mathematics, Providence University, Taichung 43301, Taiwan |
2. | Department of Mathematics, Oklahoma State University, Stillwater, OK 74078 |
[1] |
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 |
[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] |
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 |
[5] |
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 |
[6] |
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 |
[7] |
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 |
[8] |
Benjamin Dodson, Cristian Gavrus. Instability of the soliton for the focusing, mass-critical generalized KdV equation. Discrete and Continuous Dynamical Systems, 2022, 42 (4) : 1767-1799. doi: 10.3934/dcds.2021171 |
[9] |
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 |
[10] |
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 |
[11] |
Weipeng Hu, Zichen Deng, Yuyue Qin. Multi-symplectic method to simulate Soliton resonance of (2+1)-dimensional Boussinesq equation. Journal of Geometric Mechanics, 2013, 5 (3) : 295-318. doi: 10.3934/jgm.2013.5.295 |
[12] |
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 |
[13] |
M. A. Christou, C. I. Christov. Fourier-Galerkin method for localized solutions of the Sixth-Order Generalized Boussinesq Equation. Conference Publications, 2001, 2001 (Special) : 121-130. doi: 10.3934/proc.2001.2001.121 |
[14] |
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 |
[15] |
Armando Majorana. A numerical model of the Boltzmann equation related to the discontinuous Galerkin method. Kinetic and Related Models, 2011, 4 (1) : 139-151. doi: 10.3934/krm.2011.4.139 |
[16] |
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 |
[17] |
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 |
[18] |
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 |
[19] |
Ruizhi Gong, Yuren Shi, Deng-Shan Wang. Linear stability of exact solutions for the generalized Kaup-Boussinesq equation and their dynamical evolutions. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 3355-3378. doi: 10.3934/dcds.2022018 |
[20] |
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 |
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