The two-component Camassa-Holm system in weighted $L_p$ spaces
Martin Kohlmann
TL;DR
This paper establishes new persistence results for the two-component Camassa-Holm system in weighted Lp spaces, extending previous work and analyzing the solutions' spatial asymptotic behavior.
Contribution
It generalizes recent persistence results for the Camassa-Holm equation to its supersymmetric extension using weighted Lp spaces.
Findings
Persistence of solutions in weighted Lp spaces
Extension of results to supersymmetric 2CH system
Analysis of spatial asymptotic profiles
Abstract
We present some new persistence results for the non-periodic two-component Camassa-Holm (2CH) system in weighted spaces. Working with moderate weight functions that are commonly used in time-frequency analysis, the paper generalizes some recent persistence results for the Camassa-Holm equation [L. Brandolese, Int. Math. Res. Notices 22 (2012) 5161-81] to its supersymmetric extension. As an application we discuss the spatial asymptotic profile of solutions to 2CH.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Algebraic structures and combinatorial models