On the Cauchy problem for a new integrable two-component system with peakon and weak kink solutions

TL;DR

This paper investigates a new integrable two-component system, establishing local well-posedness in Besov spaces, and provides detailed blow-up scenarios and results for strong solutions with peakon and weak kink solutions.

Contribution

It introduces a novel integrable two-component system and analyzes its well-posedness and blow-up behavior, including new blow-up results for solutions.

Findings

Local well-posedness in Besov spaces

Precise blow-up scenario identified

New blow-up results for strong solutions

Abstract

This paper is contributed to study the Cauchy problem of a new integrable two-component system with peaked soliton (peakon) and weak kink solutions. We first establish the local well-posedness result for the Cauchy problem in Besov spaces, and then present a precise blow-up scenario and a new blow-up result for strong solutions to the system.