On the peakon inverse problem for the Degasperis-Procesi equation

TL;DR

This paper solves the peakon inverse problem for the Degasperis-Procesi equation directly on the real line using Cauchy biorthogonal polynomials, avoiding transformations used in previous methods.

Contribution

It introduces a novel direct approach to the inverse problem using Cauchy biorthogonal polynomials, bypassing traditional string-type boundary transformations.

Findings

Successfully solves the inverse problem directly on the real line.

Employs Cauchy biorthogonal polynomials for the first time in this context.

Provides a new method that simplifies previous approaches.

Abstract

The peakon inverse problem for the Degasperis-Procesi equation is solved directly on the real line, using Cauchy biorthogonal polynomials, without any additional transformation to a "string" type boundary value problem known from prior works.