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Stability of linear dynamic equations on time scales
The coarsegrain description of interacting sineGordon solitons with varying widths
1.  Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 602083125, United States 
2.  Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 705041010, United States 
[1] 
Christopher K. R. T. Jones, Robert Marangell. The spectrum of travelling wave solutions to the SineGordon equation. Discrete & Continuous Dynamical Systems  S, 2012, 5 (5) : 925937. doi: 10.3934/dcdss.2012.5.925 
[2] 
Goong Chen, Zhonghai Ding, Shujie Li. On positive solutions of the elliptic sineGordon equation. Communications on Pure & Applied Analysis, 2005, 4 (2) : 283294. doi: 10.3934/cpaa.2005.4.283 
[3] 
Qin Sheng, David A. Voss, Q. M. Khaliq. An adaptive splitting algorithm for the sineGordon equation. Conference Publications, 2005, 2005 (Special) : 792797. doi: 10.3934/proc.2005.2005.792 
[4] 
Igor Chueshov, Peter E. Kloeden, Meihua Yang. Synchronization in coupled stochastic sineGordon wave model. Discrete & Continuous Dynamical Systems  B, 2016, 21 (9) : 29692990. doi: 10.3934/dcdsb.2016082 
[5] 
Cornelia Schiebold. Noncommutative AKNS systems and multisoliton solutions to the matrix sinegordon equation. Conference Publications, 2009, 2009 (Special) : 678690. doi: 10.3934/proc.2009.2009.678 
[6] 
CarlFriedrich Kreiner, Johannes Zimmer. Heteroclinic travelling waves for the lattice sineGordon equation with linear pair interaction. Discrete & Continuous Dynamical Systems  A, 2009, 25 (3) : 915931. doi: 10.3934/dcds.2009.25.915 
[7] 
Shuang Yang, Yangrong Li. Forward controllability of a random attractor for the nonautonomous stochastic sineGordon equation on an unbounded domain. Evolution Equations & Control Theory, 2020, 9 (3) : 581604. doi: 10.3934/eect.2020025 
[8] 
Sara Cuenda, Niurka R. Quintero, Angel Sánchez. SineGordon wobbles through Bäcklund transformations. Discrete & Continuous Dynamical Systems  S, 2011, 4 (5) : 10471056. doi: 10.3934/dcdss.2011.4.1047 
[9] 
Gennadiy Burlak, Salomon GarcíaParedes. Matterwave solitons with a minimal number of particles in a timemodulated quasiperiodic potential. Conference Publications, 2015, 2015 (special) : 169175. doi: 10.3934/proc.2015.0169 
[10] 
Yangrong Li, Shuang Yang. Backward compact and periodic random attractors for nonautonomous sineGordon equations with multiplicative noise. Communications on Pure & Applied Analysis, 2019, 18 (3) : 11551175. doi: 10.3934/cpaa.2019056 
[11] 
V. V. Chepyzhov, M. I. Vishik, W. L. Wendland. On nonautonomous sineGordon type equations with a simple global attractor and some averaging. Discrete & Continuous Dynamical Systems  A, 2005, 12 (1) : 2738. doi: 10.3934/dcds.2005.12.27 
[12] 
ChiKun Lin, KungChien Wu. On the fluid dynamical approximation to the nonlinear KleinGordon equation. Discrete & Continuous Dynamical Systems  A, 2012, 32 (6) : 22332251. doi: 10.3934/dcds.2012.32.2233 
[13] 
Yanling Shi, Junxiang Xu. Quasiperiodic solutions for nonlinear wave equation with Liouvillean frequency. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020241 
[14] 
Andrzej Nowakowski. Variational approach to stability of semilinear wave equation with nonlinear boundary conditions. Discrete & Continuous Dynamical Systems  B, 2014, 19 (8) : 26032616. doi: 10.3934/dcdsb.2014.19.2603 
[15] 
Alexander Komech, Elena Kopylova, David Stuart. On asymptotic stability of solitons in a nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2012, 11 (3) : 10631079. doi: 10.3934/cpaa.2012.11.1063 
[16] 
Yusuke Murase, Atsushi Kadoya, Nobuyuki Kenmochi. Optimal control problems for quasivariational inequalities and its numerical approximation. Conference Publications, 2011, 2011 (Special) : 11011110. doi: 10.3934/proc.2011.2011.1101 
[17] 
Gong Chen, Peter J. Olver. Numerical simulation of nonlinear dispersive quantization. Discrete & Continuous Dynamical Systems  A, 2014, 34 (3) : 9911008. doi: 10.3934/dcds.2014.34.991 
[18] 
Walid K. Abou Salem, Xiao Liu, Catherine Sulem. Numerical simulation of resonant tunneling of fast solitons for the nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems  A, 2011, 29 (4) : 16371649. doi: 10.3934/dcds.2011.29.1637 
[19] 
Christopher Chong, Dmitry Pelinovsky. Variational approximations of bifurcations of asymmetric solitons in cubicquintic nonlinear Schrödinger lattices. Discrete & Continuous Dynamical Systems  S, 2011, 4 (5) : 10191031. doi: 10.3934/dcdss.2011.4.1019 
[20] 
TaiChia Lin. Vortices for the nonlinear wave equation. Discrete & Continuous Dynamical Systems  A, 1999, 5 (2) : 391398. doi: 10.3934/dcds.1999.5.391 
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