The N-soliton solution of a two-component modified nonlinear Schr\"odinger equation

TL;DR

This paper derives explicit N-soliton solutions for a two-component modified nonlinear Schrödinger equation relevant to optical fibers, using determinant methods, and discusses multi-component generalizations and higher-dimensional limits.

Contribution

It provides the first explicit determinant-based N-soliton solutions for the two-component modified nonlinear Schrödinger equation.

Findings

Explicit N-soliton solutions expressed in determinants.

Methodology based on elementary determinant theory.

Discussion on multi-component and higher-dimensional generalizations.

Abstract

The $N$-soliton solution is presented for a two-component modified nonlinear Schr\"odinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit.