The resonant structure of Kink-Solitons in the Modified KP Equation

TL;DR

This paper explores the resonant structures of kink- and line-solitons in the modified KP equation using Wronskian representations, revealing how these structures relate to superimposed soliton graphs derived from Le-Diagrams in Grassmannians.

Contribution

It introduces a novel method to analyze resonant soliton structures via superimposed graphs from Le-Diagrams, connecting soliton theory with algebraic geometry.

Findings

Resonant structures correspond to superimposed soliton graphs.

The approach links soliton configurations to totally non-negative Grassmannians.

Several explicit examples illustrate the theoretical framework.

Abstract

Using the Wronskian representation of $\tau$-function, one can investigate the resonant structure of kink-soliton and line-soliton of the modified KP equation. It is found that the resonant structure of the the soliton graph is obtained by superimposition of the two corresponding soliton graphs of the two Le-Diagrams given an irreducible Schubert cell in a totally non-negative Grassmannian $Gr(N,M)_{ \geq 0}$. Several examples are given.