The variable-length stem structures in three-soliton resonance of the Kadomtsev-Petviashvili II equation

TL;DR

This paper studies the variable-length stem structures in three-soliton resonance solutions of the KPII equation, analyzing their asymptotic behavior, explicit forms, and differences in 2-resonant and 3-resonant cases.

Contribution

It provides a detailed analysis of stem structures in resonant 3-solitons, including explicit expressions and asymptotic analysis, highlighting differences between 2-resonant and 3-resonant cases.

Findings

Identification of different resonance types based on phase shifts

Explicit formulas for soliton trajectories and stem properties

Comparison of stem structures in 2-resonant and 3-resonant cases

Abstract

The stem structure is a localized feature that arises during high-order soliton interactions, connecting the vertices of two V-shaped waveforms. The interaction of resonant 3-solitons is accompanied by soliton reconnection phenomena, characterized by the disappearance and reconnection of stem structures. This paper investigates variable-length stem structures in resonant 3-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation, focusing on both 2-resonant and 3-resonant 3-soliton cases. Depending on the phase shift tends to plus/minus infinity, different types of resonances are identified, including strong resonance, weak resonance, and mixed (strong-weak) resonance. We derive and analyze the asymptotic forms and explicit expressions for the soliton arm trajectories, velocities, as well as the endpoints, length, and amplitude of the stem structures. A detailed comparison is made between the similarities and differences of the stem structures in the 2-resonant and 3-resonant solitons. In addition, we provide a comprehensive and rigorous analysis of both the asymptotic behavior and the structural properties of the stems.