Soliton-like solutions of the modified Camassa-Holm equation with variable coefficients
Résumé
We study soliton- and peakon-like solutions of the modified Camassa-Holm equation with variable coefficients and a singular perturbation. This equation is a direct generalization of the well-known modified Camassa-Holm equation, which is an integrable system having both smooth and peaked soliton solutions, named peakons. The novelty of this paper lies in the development of a general methodology for constructing asymptotic peakon-like solutions. We present a general scheme for finding approximations of any order and study their accuracy. The results are illustrated by nontrivial examples of both soliton- and peakon-like solutions with global phase function. The proposed technique can be used for studying wave-like solutions of other equations with variable coefficients and small dispersion.
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