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On the local solvability of Darboux's equation
A dualPetrovGalerkin method for extended fifthorder Kortewegde Vries type equations
1.  Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States, United States, United States 
[1] 
JuanMing Yuan, Jiahong Wu. A dualPetrovGalerkin method for two integrable fifthorder KdV type equations. Discrete & Continuous Dynamical Systems  A, 2010, 26 (4) : 15251536. doi: 10.3934/dcds.2010.26.1525 
[2] 
Marina Chugunova, Dmitry Pelinovsky. Twopulse solutions in the fifthorder KdV equation: Rigorous theory and numerical approximations. Discrete & Continuous Dynamical Systems  B, 2007, 8 (4) : 773800. doi: 10.3934/dcdsb.2007.8.773 
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Yingte Sun, Xiaoping Yuan. Quasiperiodic solution of quasilinear fifthorder KdV equation. Discrete & Continuous Dynamical Systems  A, 2018, 38 (12) : 62416285. doi: 10.3934/dcds.2018268 
[4] 
Torsten Keßler, Sergej Rjasanow. Fully conservative spectral Galerkin–Petrov method for the inhomogeneous Boltzmann equation. Kinetic & Related Models, 2019, 12 (3) : 507549. doi: 10.3934/krm.2019021 
[5] 
Jie Shen, LiLian Wang. Laguerre and composite LegendreLaguerre DualPetrovGalerkin methods for thirdorder equations. Discrete & Continuous Dynamical Systems  B, 2006, 6 (6) : 13811402. doi: 10.3934/dcdsb.2006.6.1381 
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Jibin Li, Yi Zhang. Exact solitary wave and quasiperiodic wave solutions for four fifthorder nonlinear wave equations. Discrete & Continuous Dynamical Systems  B, 2010, 13 (3) : 623631. doi: 10.3934/dcdsb.2010.13.623 
[7] 
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 & Related Models, 2019, 12 (4) : 909922. doi: 10.3934/krm.2019034 
[8] 
Pedro Isaza, Juan López, Jorge Mejía. Cauchy problem for the fifth order KadomtsevPetviashvili (KPII) equation. Communications on Pure & Applied Analysis, 2006, 5 (4) : 887905. doi: 10.3934/cpaa.2006.5.887 
[9] 
Jerry L. Bona, Didier Pilod. Stability of solitarywave solutions to the HirotaSatsuma equation. Discrete & Continuous Dynamical Systems  A, 2010, 27 (4) : 13911413. doi: 10.3934/dcds.2010.27.1391 
[10] 
Hisashi Okamoto, Takashi Sakajo, Marcus Wunsch. Steadystates and travelingwave solutions of the generalized ConstantinLaxMajda equation. Discrete & Continuous Dynamical Systems  A, 2014, 34 (8) : 31553170. doi: 10.3934/dcds.2014.34.3155 
[11] 
Út V. Lê. ContractionGalerkin method for a semilinear wave equation. Communications on Pure & Applied Analysis, 2010, 9 (1) : 141160. doi: 10.3934/cpaa.2010.9.141 
[12] 
Márcio Cavalcante, Chulkwang Kwak. Local wellposedness of the fifthorder KdVtype equations on the halfline. Communications on Pure & Applied Analysis, 2019, 18 (5) : 26072661. doi: 10.3934/cpaa.2019117 
[13] 
JuanMing Yuan, Jiahong Wu. The complex KdV equation with or without dissipation. Discrete & Continuous Dynamical Systems  B, 2005, 5 (2) : 489512. doi: 10.3934/dcdsb.2005.5.489 
[14] 
Liu Liu. Uniform spectral convergence of the stochastic Galerkin method for the linear semiconductor Boltzmann equation with random inputs and diffusive scaling. Kinetic & Related Models, 2018, 11 (5) : 11391156. doi: 10.3934/krm.2018044 
[15] 
Yiren Chen, Zhengrong Liu. The bifurcations of solitary and kink waves described by the Gardner equation. Discrete & Continuous Dynamical Systems  S, 2016, 9 (6) : 16291645. doi: 10.3934/dcdss.2016067 
[16] 
H. Kalisch. Stability of solitary waves for a nonlinearly dispersive equation. Discrete & Continuous Dynamical Systems  A, 2004, 10 (3) : 709717. doi: 10.3934/dcds.2004.10.709 
[17] 
Lingbing He, Yulong Zhou. High order approximation for the Boltzmann equation without angular cutoff. Kinetic & Related Models, 2018, 11 (3) : 547596. doi: 10.3934/krm.2018024 
[18] 
Rowan Killip, Soonsik Kwon, Shuanglin Shao, Monica Visan. On the masscritical generalized KdV equation. Discrete & Continuous Dynamical Systems  A, 2012, 32 (1) : 191221. doi: 10.3934/dcds.2012.32.191 
[19] 
Annie Millet, Svetlana Roudenko. Generalized KdV equation subject to a stochastic perturbation. Discrete & Continuous Dynamical Systems  B, 2018, 23 (3) : 11771198. doi: 10.3934/dcdsb.2018147 
[20] 
S. Raynor, G. Staffilani. Low regularity stability of solitons for the KDV equation. Communications on Pure & Applied Analysis, 2003, 2 (3) : 277296. doi: 10.3934/cpaa.2003.2.277 
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