The bright $N$-soliton solution of a multi-component modified nonlinear Schrödinger equation

Abstract

A direct method is developed for constructing the bright $N$-soliton solution of a multi-component modified nonlinear Schrödinger 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.

To appear in J. Phys. A: Math. Theor

References in corpus (1)

• Localized Solitons of a (2+1)-dimensional Nonlocal Nonlinear Schrödinger Equation

Cited by in corpus (4)

• A direct method of solution for the Fokas-Lenells derivative nonlinear Schrödinger equation: I. Bright soliton solutions
• Riemann-Hilbert approach to the modified nonlinear Schröinger equation with non-vanishing asymptotic boundary conditions
• The multi-component modified nonlinear Schrödinger system with nonzero boundary conditions
• The coupled modified nonlinear Schrödinger equations on the half-line via the Fokas method