Akhmediev breathers, Ma solitons and general breathers from rogue waves: A case study in Manakov system

TL;DR

This paper derives explicit breather, soliton, and rogue wave solutions for the two-component Manakov system using two different methods, enhancing understanding of these solutions in multi-component nonlinear Schrödinger equations.

Contribution

It introduces a novel two-route approach to derive rational solutions of the Manakov system, linking them to scalar NLS solutions with modified nonlinearity.

Findings

Explicit solutions for GB, AB, MS, and RW in the Manakov system.

Demonstrates derivation of solutions from scalar NLS with modified parameters.

Provides a broader understanding of rational solutions in multi-component systems.

Abstract

We present explicit forms of general breather (GB), Akhmediev breather (AB), Ma soliton (MS) and rogue wave (RW) solutions of the two component nonlinear Schr\"{o}dinger (NLS) equation, namely Manakov equation. We derive these solutions through two different routes. In the forward route we first construct a suitable periodic envelope soliton solution to this model from which we derive GB, AB, MS and RW solutions. We then consider the RW solution as the starting point and derive AB, MS and GB in the reverse direction. The second approach has not been illustrated so far for the two component NLS equation. Our results show that the above rational solutions of the Manakov system can be derived from the standard scalar nonlinear Schr\"{o}dinger equation with a modified nonlinearity parameter. Through this two way approach we establish a broader understanding of these rational solutions which will be of interest in a variety of situations.