The bright $N$-soliton solution of a multi-component modified nonlinear Schr\"odinger equation

TL;DR

This paper develops a direct method to construct bright N-soliton solutions for a multi-component modified nonlinear Schrödinger equation, expressing solutions as determinants and exploring their relations.

Contribution

It introduces a novel determinant-based approach for multi-component soliton solutions and connects different solution expressions through properties of the Cauchy matrix.

Findings

Derived two determinant expressions for solutions

Established relations between solution forms using Cauchy matrix properties

Presented N-soliton solutions for a (2+1)-D nonlocal model

Abstract

A direct method is developed for constructing the bright $N$-soliton solution of a multi-component modified nonlinear Schr\"odinger equation. Specifically, the two different expressions of the solution are obtained both of which are expressed as a rational function of determinants. A simple relation is found between them by employing the properties of the Cauchy matrix. The proof of the solution reduces to the bilinear equations among the bordered determinants in which Jacobi's identity and related formulas play a central role. Last, the bright $N$-soliton solution is presented for a (2+1)-dimensional nonlocal model equation arising from the multi-component system as the number of dependent variables tends to infinity.