Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schr\"odinger equations

TL;DR

This paper derives bright-dark soliton solutions for mixed focusing and defocusing N-coupled nonlinear Schrödinger equations, analyzing their collision dynamics and revealing complex interactions including shape changes and phase shifts.

Contribution

It introduces a systematic method to obtain mixed soliton solutions and analyzes their collision behavior in multi-component systems, highlighting novel interaction effects.

Findings

Bright solitons exhibit shape-changing collisions with amplitude-dependent phase shifts.

Dark solitons undergo elastic collisions with amplitude-dependent phase shifts.

Interactions between bright and dark solitons influence each other's collision dynamics.

Abstract

Mixed type (bright-dark) soliton solutions of the integrable N-coupled nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients are obtained by using Hirota's bilinearization method. Generally, for the mixed N-CNLS equations the bright and dark solitons can be split up in $(N-1)$ ways. By analysing the collision dynamics of these coupled bright and dark solitons systematically we point out that for $N>2$, if the bright solitons appear in at least two components, non-trivial effects like onset of intensity redistribution, amplitude dependent phase-shift and change in relative separation distance take place in the bright solitons during collision. However their counterparts, the dark solitons, undergo elastic collision but experience the same amplitude dependent phase-shift as that of bright solitons. Thus in the mixed CNLS system there co-exist shape changing collision of bright solitons and elastic collision of dark solitons with amplitude dependent phase-shift, thereby influencing each other mutually in an intricate way.