Degenerate Four Virtual Soliton Resonance for KP-II

TL;DR

This paper introduces a novel bilinear representation for the KP-II equation using dissipative AKNS hierarchy members, leading to the first virtual soliton resonance solutions and insights into their interactions.

Contribution

It develops a new bilinear form for KP-II based on dissipative AKNS flows, enabling the construction of virtual soliton resonance solutions and linking them to degenerate four-soliton solutions.

Findings

First virtual soliton resonance solutions for KP-II

New bilinear representation for KP-II

Relations established between virtual and degenerate four-soliton solutions

Abstract

By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional Kadomtsev-Petviashvili (KP-II) equation is proposed. We show that dissipative solitons (dissipatons) of those members give rise to the real solitons of KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for KP-II, by which, one and two soliton solutions are constructed and the resonance character of their mutual interactions is studied. By our bilinear form, we first time created four virtual soliton resonance solution for KP-II and established relations of it with degenerate four-soliton solution in the Hirota-Satsuma bilinear form for KP-II.