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The longtime behaviour for nonlinear Schrödinger equation and its rational pseudospectral approximation
The complex KdV equation with or without dissipation
1.  Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States 
[1] 
Jerry L. Bona, Stéphane Vento, Fred B. Weissler. Singularity formation and blowup of complexvalued solutions of the modified KdV equation. Discrete & Continuous Dynamical Systems  A, 2013, 33 (11&12) : 48114840. doi: 10.3934/dcds.2013.33.4811 
[2] 
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 
[3] 
Yuqian Zhou, Qian Liu. Reduction and bifurcation of traveling waves of the KdVBurgersKuramoto equation. Discrete & Continuous Dynamical Systems  B, 2016, 21 (6) : 20572071. doi: 10.3934/dcdsb.2016036 
[4] 
Zhaosheng Feng, Qingguo Meng. Exact solution for a twodimensional KDVBurgerstype equation with nonlinear terms of any order. Discrete & Continuous Dynamical Systems  B, 2007, 7 (2) : 285291. doi: 10.3934/dcdsb.2007.7.285 
[5] 
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 
[6] 
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 
[7] 
María Santos Bruzón, Tamara María Garrido. Symmetries and conservation laws of a KdV6 equation. Discrete & Continuous Dynamical Systems  S, 2018, 11 (4) : 631641. doi: 10.3934/dcdss.2018038 
[8] 
Gianluca FrascaCaccia, Peter E. Hydon. Locally conservative finite difference schemes for the modified KdV equation. Journal of Computational Dynamics, 2019, 6 (2) : 307323. doi: 10.3934/jcd.2019015 
[9] 
Jongmin Han, Masoud Yari. Dynamic bifurcation of the complex SwiftHohenberg equation. Discrete & Continuous Dynamical Systems  B, 2009, 11 (4) : 875891. doi: 10.3934/dcdsb.2009.11.875 
[10] 
Mostafa Abounouh, Olivier Goubet. Regularity of the attractor for kp1Burgers equation: the periodic case. Communications on Pure & Applied Analysis, 2004, 3 (2) : 237252. doi: 10.3934/cpaa.2004.3.237 
[11] 
Ademir Fernando Pazoto, Lionel Rosier. Uniform stabilization in weighted Sobolev spaces for the KdV equation posed on the halfline. Discrete & Continuous Dynamical Systems  B, 2010, 14 (4) : 15111535. doi: 10.3934/dcdsb.2010.14.1511 
[12] 
MaríaSantos Bruzón, Elena Recio, TamaraMaría Garrido, Rafael de la Rosa. Lie symmetries, conservation laws and exact solutions of a generalized quasilinear KdV equation with degenerate dispersion. Discrete & Continuous Dynamical Systems  S, 2020, 13 (10) : 26912701. doi: 10.3934/dcdss.2020222 
[13] 
Mamoru Okamoto. Asymptotic behavior of solutions to a higherorder KdVtype equation with critical nonlinearity. Evolution Equations & Control Theory, 2019, 8 (3) : 567601. doi: 10.3934/eect.2019027 
[14] 
Jerry L. Bona, Hongqiu Chen, ShuMing Sun, BingYu Zhang. Comparison of quarterplane and twopoint boundary value problems: The KdVequation. Discrete & Continuous Dynamical Systems  B, 2007, 7 (3) : 465495. doi: 10.3934/dcdsb.2007.7.465 
[15] 
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 
[16] 
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 
[17] 
Na An, Chaobao Huang, Xijun Yu. Error analysis of discontinuous Galerkin method for the time fractional KdV equation with weak singularity solution. Discrete & Continuous Dynamical Systems  B, 2020, 25 (1) : 321334. doi: 10.3934/dcdsb.2019185 
[18] 
Kotaro Tsugawa. Existence of the global attractor for weakly damped, forced KdV equation on Sobolev spaces of negative index. Communications on Pure & Applied Analysis, 2004, 3 (2) : 301318. doi: 10.3934/cpaa.2004.3.301 
[19] 
Hans G. Kaper, Peter Takáč. Bifurcating vortex solutions of the complex GinzburgLandau equation. Discrete & Continuous Dynamical Systems  A, 1999, 5 (4) : 871880. doi: 10.3934/dcds.1999.5.871 
[20] 
Jungho Park. Bifurcation and stability of the generalized complex GinzburgLandau equation. Communications on Pure & Applied Analysis, 2008, 7 (5) : 12371253. doi: 10.3934/cpaa.2008.7.1237 
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