Soliton Resonances for MKP-II

TL;DR

This paper derives soliton solutions for the MKP-II equation using bilinear forms from related integrable systems, revealing resonance phenomena and interpreting resonant solitons as composites of dissipative solitons.

Contribution

It constructs Hirota's bilinear representation for MKP-II from the Derivative Reaction-Diffusion and Kaup-Newell hierarchies, enabling explicit soliton solutions and resonance analysis.

Findings

Found one and two soliton solutions for MKP-II.

Demonstrated resonance behavior with virtual soliton creation.

Interpreted resonance solitons as composites of dissipative solitons.

Abstract

Using the second flow - the Derivative Reaction-Diffusion system, and the third one of the dissipative SL(2,R) Kaup-Newell hierarchy, we show that the product of two functions, satisfying those systems is a solution of the modified Kadomtsev-Petviashvili equation in 2+1 dimension with negative dispersion (MKP-II). We construct Hirota's bilinear representation for both flows and combine them together as the bilinear system for MKP-II. Using this bilinear form we find one and two soliton solutions for the MKP-II. For special values of parameters our solution shows resonance behaviour with creation of four virtual solitons. Our approach allows one to interpret the resonance soliton as a composite object of two dissipative solitons in 1+1 dimensions.