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Twopulse solutions in the fifthorder KdV equation: Rigorous theory and numerical approximations
1.  Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada, Canada 
[1] 
JuanMing Yuan, Jiahong Wu. A dualPetrovGalerkin method for two integrable fifthorder KdV type equations. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 15251536. doi: 10.3934/dcds.2010.26.1525 
[2] 
Yingte Sun, Xiaoping Yuan. Quasiperiodic solution of quasilinear fifthorder KdV equation. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : 62416285. doi: 10.3934/dcds.2018268 
[3] 
Jibin Li, Yi Zhang. Exact solitary wave and quasiperiodic wave solutions for four fifthorder nonlinear wave equations. Discrete and Continuous Dynamical Systems  B, 2010, 13 (3) : 623631. doi: 10.3934/dcdsb.2010.13.623 
[4] 
Márcio Cavalcante, Chulkwang Kwak. Local wellposedness of the fifthorder KdVtype equations on the halfline. Communications on Pure and Applied Analysis, 2019, 18 (5) : 26072661. doi: 10.3934/cpaa.2019117 
[5] 
Pedro Isaza, Juan López, Jorge Mejía. Cauchy problem for the fifth order KadomtsevPetviashvili (KPII) equation. Communications on Pure and Applied Analysis, 2006, 5 (4) : 887905. doi: 10.3934/cpaa.2006.5.887 
[6] 
Netra Khanal, Ramjee Sharma, Jiahong Wu, JuanMing Yuan. A dualPetrovGalerkin method for extended fifthorder Kortewegde Vries type equations. Conference Publications, 2009, 2009 (Special) : 442450. doi: 10.3934/proc.2009.2009.442 
[7] 
Willem M. SchoutenStraatman, Hermen Jan Hupkes. Nonlinear stability of pulse solutions for the discrete FitzHughNagumo equation with infiniterange interactions. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 50175083. doi: 10.3934/dcds.2019205 
[8] 
Zhaosheng Feng, Qingguo Meng. Exact solution for a twodimensional KDVBurgerstype equation with nonlinear terms of any order. Discrete and Continuous Dynamical Systems  B, 2007, 7 (2) : 285291. 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] 
Junichi 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) : 843859. 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) : 801821. doi: 10.3934/dcds.2008.21.801 
[12] 
Jerry L. Bona, Angel Durán, Dimitrios Mitsotakis. Solitarywave solutions of BenjaminOno and other systems for internal waves. I. approximations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 87111. 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) : 737753. doi: 10.3934/eect.2019036 
[14] 
Anwar Ja'afar Mohamad Jawad, Mohammad Mirzazadeh, Anjan Biswas. Dynamics of shallow water waves with GardnerKadomtsevPetviashvili equation. Discrete and Continuous Dynamical Systems  S, 2015, 8 (6) : 11551164. 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) : 1124. 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) : 10871104. doi: 10.3934/cpaa.2014.13.1087 
[17] 
Mamoru Okamoto. Asymptotic behavior of solutions to a higherorder KdVtype equation with critical nonlinearity. Evolution Equations and Control Theory, 2019, 8 (3) : 567601. 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) : 277296. 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) : 525544. 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) : 12291247. doi: 10.3934/dcds.2009.25.1229 
2020 Impact Factor: 1.327
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