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Stability of linear dynamic equations on time scales
The coarse-grain description of interacting sine-Gordon solitons with varying widths
1. | Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208-3125, United States |
2. | Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, United States |
[1] |
Christopher K. R. T. Jones, Robert Marangell. The spectrum of travelling wave solutions to the Sine-Gordon equation. Discrete and Continuous Dynamical Systems - S, 2012, 5 (5) : 925-937. doi: 10.3934/dcdss.2012.5.925 |
[2] |
Goong Chen, Zhonghai Ding, Shujie Li. On positive solutions of the elliptic sine-Gordon equation. Communications on Pure and Applied Analysis, 2005, 4 (2) : 283-294. doi: 10.3934/cpaa.2005.4.283 |
[3] |
Qin Sheng, David A. Voss, Q. M. Khaliq. An adaptive splitting algorithm for the sine-Gordon equation. Conference Publications, 2005, 2005 (Special) : 792-797. doi: 10.3934/proc.2005.2005.792 |
[4] |
Igor Chueshov, Peter E. Kloeden, Meihua Yang. Synchronization in coupled stochastic sine-Gordon wave model. Discrete and Continuous Dynamical Systems - B, 2016, 21 (9) : 2969-2990. doi: 10.3934/dcdsb.2016082 |
[5] |
Cornelia Schiebold. Noncommutative AKNS systems and multisoliton solutions to the matrix sine-gordon equation. Conference Publications, 2009, 2009 (Special) : 678-690. doi: 10.3934/proc.2009.2009.678 |
[6] |
Carl-Friedrich Kreiner, Johannes Zimmer. Heteroclinic travelling waves for the lattice sine-Gordon equation with linear pair interaction. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 915-931. doi: 10.3934/dcds.2009.25.915 |
[7] |
Shuang Yang, Yangrong Li. Forward controllability of a random attractor for the non-autonomous stochastic sine-Gordon equation on an unbounded domain. Evolution Equations and Control Theory, 2020, 9 (3) : 581-604. doi: 10.3934/eect.2020025 |
[8] |
Hang Zheng, Yonghui Xia, Manuel Pinto. Chaotic motion and control of the driven-damped Double Sine-Gordon equation. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022037 |
[9] |
Sara Cuenda, Niurka R. Quintero, Angel Sánchez. Sine-Gordon wobbles through Bäcklund transformations. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1047-1056. doi: 10.3934/dcdss.2011.4.1047 |
[10] |
Gennadiy Burlak, Salomon García-Paredes. Matter-wave solitons with a minimal number of particles in a time-modulated quasi-periodic potential. Conference Publications, 2015, 2015 (special) : 169-175. doi: 10.3934/proc.2015.0169 |
[11] |
Yangrong Li, Shuang Yang. Backward compact and periodic random attractors for non-autonomous sine-Gordon equations with multiplicative noise. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1155-1175. doi: 10.3934/cpaa.2019056 |
[12] |
V. V. Chepyzhov, M. I. Vishik, W. L. Wendland. On non-autonomous sine-Gordon type equations with a simple global attractor and some averaging. Discrete and Continuous Dynamical Systems, 2005, 12 (1) : 27-38. doi: 10.3934/dcds.2005.12.27 |
[13] |
Chi-Kun Lin, Kung-Chien Wu. On the fluid dynamical approximation to the nonlinear Klein-Gordon equation. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 2233-2251. doi: 10.3934/dcds.2012.32.2233 |
[14] |
Yanling Shi, Junxiang Xu. Quasi-periodic solutions for nonlinear wave equation with Liouvillean frequency. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3479-3490. doi: 10.3934/dcdsb.2020241 |
[15] |
Andrzej Nowakowski. Variational approach to stability of semilinear wave equation with nonlinear boundary conditions. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2603-2616. doi: 10.3934/dcdsb.2014.19.2603 |
[16] |
Alexander Komech, Elena Kopylova, David Stuart. On asymptotic stability of solitons in a nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1063-1079. doi: 10.3934/cpaa.2012.11.1063 |
[17] |
Yusuke Murase, Atsushi Kadoya, Nobuyuki Kenmochi. Optimal control problems for quasi-variational inequalities and its numerical approximation. Conference Publications, 2011, 2011 (Special) : 1101-1110. doi: 10.3934/proc.2011.2011.1101 |
[18] |
Gong Chen, Peter J. Olver. Numerical simulation of nonlinear dispersive quantization. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 991-1008. doi: 10.3934/dcds.2014.34.991 |
[19] |
Walid K. Abou Salem, Xiao Liu, Catherine Sulem. Numerical simulation of resonant tunneling of fast solitons for the nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 1637-1649. doi: 10.3934/dcds.2011.29.1637 |
[20] |
Christopher Chong, Dmitry Pelinovsky. Variational approximations of bifurcations of asymmetric solitons in cubic-quintic nonlinear Schrödinger lattices. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1019-1031. doi: 10.3934/dcdss.2011.4.1019 |
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