2011/06/03 by Claudio Muñoz, Muñoz, Claudio
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP
paper · pdf · doi:10.48550/arxiv.1106.0648
34 pages, 4 figures, some typos corrected
arxiv created 2011/08/09 · arxiv updated 2011/08/10
Multi-kink solutions of the defocusing, modified Korteweg-de Vries equation (mKdV) found by Grosse are shown to be globally H1-stable. Stability in the one-kink case was previously established by Zhidkov, and Merle-Vega. 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, uniqueness and the dynamics of generalized multi-kinks of defocusing, non-integrable gKdV equations, showing the inelastic character of the 4-kink collision in some regimes.