The Mechanism of Kuznetsov-Ma Breather

TL;DR

This paper explores the physical mechanisms behind the Kuznetsov-Ma breather, highlighting the roles of modulational instability and interference effects in its dynamical evolution.

Contribution

It provides a detailed analysis of the physical mechanisms governing Kuznetsov-Ma breather dynamics, emphasizing the interplay of modulational instability and interference effects.

Findings

Modulational instability dominates with weak perturbations.

Interference effects are key for strong perturbations.

Both mechanisms are significant in intermediate cases.

Abstract

We discuss how to understand the dynamical process of Kuznetsov-Ma breather, based on some basic physical mechanisms. It is shown that dynamical process of Kuznetsov-Ma breather involves at least two distinctive mechanisms: modulational instability, and the interference effects between a bright soliton and a plane wave background. Our analysis indicates that modulational instability plays dominant roles in mechanism of Kuznetsov-Ma breather admitting weak perturbations, and the interference effect plays dominant role for the Kuznetsov-Ma breather admitting strong perturbations. For intermediate cases, the two mechanisms are both involved greatly. These characters provide a possible way to understand the evolution of strong perturbations on a plane wave background.