The Effect of the Elliptic Polarization on the Quasi-particle Dynamics of Linearly Coupled Systems of Nonlinear Schroedinger Equations

TL;DR

This paper numerically studies how elliptic polarization influences the dynamics and interactions of solitary waves in linearly coupled nonlinear Schrödinger equations, revealing polarization effects on conservation laws and quasi-particle behavior.

Contribution

It introduces a numerical analysis of polarization effects on solitary wave interactions in coupled nonlinear Schrödinger systems, highlighting polarization angle independence and conservation properties.

Findings

Total mass, pseudomomentum, and energy are conserved.

Local masses and polarization depend on coupling and initial phase.

Polarization angle can change independently of interactions.

Abstract

We investigate numerically by a conservative difference scheme in complex arithmetic the head-on and takeover collision dynamics of the solitary waves as solutions of linearly Coupled Nonlinear Schr\"odinger Equations for various initial phases. The initial conditions are superposition of two one-soliton solutions with general polarization. The quasi-particle behavior of propagating and interacting solutions in conditions of rotational polarization is examined. We find that the total mass, pseudomomentum and energy are conserved while the local masses, individual and total polarization depend strongly on the linear coupling and the initial phase difference. We also find out that the polarization angle of the quasi-particles can change independently of the interaction.