Nondegenerate soliton solutions in certain coupled nonlinear Schr\"{o}dinger systems

TL;DR

This paper introduces a broader class of nondegenerate soliton solutions with distinct wave numbers for coupled nonlinear Schrödinger systems, revealing novel profiles and connecting to known degenerate solutions.

Contribution

The paper derives a more general form of nondegenerate soliton solutions for coupled NLS systems, highlighting novel profiles and their relation to degenerate solutions.

Findings

Derived general nondegenerate soliton solutions for coupled NLS equations.

Revealed novel soliton profile structures distinct from degenerate solutions.

Showed how degenerate solutions are limiting cases of nondegenerate solutions.

Abstract

In this paper, we report a more general class of nondegenerate soliton solutions, associated with two distinct wave numbers in different modes, for a certain class of physically important integrable two component nonlinear Schr\"{o}dinger type equations through bilinearization procedure. In particular, we consider coupled nonlinear Schr\"{o}dinger (CNLS) equations (both focusing as well as mixed type nonlinearities), coherently coupled nonlinear Schr\"{o}dinger (CCNLS) equations and long-wave-short-wave resonance interaction (LSRI) system. We point out that the obtained general form of soliton solutions exhibit novel profile structures than the previously known degenerate soliton solutions corresponding to identical wave numbers in both the modes. We show that such degenerate soliton solutions can be recovered from the newly derived nondegenerate soliton solutions as limiting cases.