The Gardner equation and the stability of multi-kink solutions of the mKdV equation

Claudio Muñoz
2016 Discrete and Continuous Dynamical Systems. Series A  
Multi-kink solutions of the defocusing, modified Korteweg-de Vries equation (mKdV) found by Grosse [22, 23] are shown to be globally H 1 -stable, and asymptotically stable. Stability in the one-kink case was previously established by Zhidkov [51] and Merle-Vega [41] . The proof uses transformations linking the mKdV equation with focusing, Gardner-like equations, where stability and asymptotic stability in the energy space are known. We generalize our results by considering the existence,
more » ... ess and the dynamics of generalized multi-kinks of defocusing, non-integrable gKdV equations, showing the inelastic character of the kink-kink collision in some regimes.
doi:10.3934/dcds.2016.36.3811 fatcat:cgauj3tkd5g7pg5ezkeumddcry