Localized stem structures in quasi-resonant two-soliton solutions for the asymmetric Nizhnik-Novikov-Veselov system

TL;DR

This paper investigates the formation and properties of localized stem structures connecting two solitons during quasi-resonant collisions in the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, revealing their spatial and temporal invariance.

Contribution

It systematically analyzes the characteristics of stem structures in quasi-resonant soliton collisions, providing new insights into their trajectories, amplitudes, and lengths in the system.

Findings

Stem structures exhibit spatial locality and temporal invariance.

Different behaviors are observed under weak and strong quasi-resonance.

Mathematical analysis reveals detailed soliton trajectories and amplitudes.

Abstract

Elastic collisions of solitons generally have a finite phase shift. When the phase shift has a finitely large value, the two vertices of the (2+1)-dimensional 2-soliton are significantly separated due to the phase shift, accompanied by the formation of a local structure connecting the two V-shaped solitons. We define this local structure as the stem structure. This study systematically investigates the localized stem structures between two solitons in the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system. These stem structures, arising from quasi-resonant collisions between the solitons, exhibit distinct features of spatial locality and temporal invariance. We explore two scenarios: one characterized by weakly quasi-resonant collisions (i.e. $a_{12}\approx 0$), and the other by strongly quasi-resonant collisions (i.e. $a_{12}\approx +\infty$). Through mathematical analysis, we extract comprehensive insights into the trajectories, amplitudes, and velocities of the soliton arms. Furthermore, we discuss the characteristics of the stem structures, including their length and extreme points. Our findings shed new light on the interaction between solitons in the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system.