An inverse problem for the modified Camassa-Holm equation and multi-point Pad\'{e} approximants

TL;DR

This paper explores the inverse spectral method for constructing non-smooth solitons of the modified Camassa-Holm equation, demonstrating that the inverse problem can be solved using multi-point Padé approximations.

Contribution

It introduces a novel approach linking inverse spectral problems for the modified Camassa-Holm equation with multi-point Padé approximations.

Findings

Inverse problem is solvable via multi-point Padé approximations.

Constructs non-smooth solitons (peakons) for the modified Camassa-Holm equation.

Provides a spectral method framework for soliton solutions.

Abstract

In this Letter the main steps in the inverse spectral construction of a family of non-smooth solitons (peakons) to the modified Camassa-Holm equation are oulined. It is shown that the inverse problem is solvable in terms of multi-point Pad\'{e} approximations.