The concept of quasi-integrability for modified non-linear Schrodinger models

TL;DR

This paper explores quasi-integrability in modified nonlinear Schrödinger models, demonstrating the existence of quasi-conserved charges and analyzing soliton scattering through analytical and numerical methods, with potential implications across nonlinear science.

Contribution

It introduces the concept of quasi-integrability in modified NLS models and shows these models possess quasi-conserved charges related to specific parity transformations.

Findings

Quasi-conserved charges are asymptotically conserved during soliton scattering.

Numerical simulations confirm analytical predictions for modified NLS potentials.

Quasi-integrability extends to perturbations of the sine-Gordon model.

Abstract

We consider modifications of the nonlinear Schrodinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an infinite number of quasi-conserved charges which present intriguing properties in relation to very specific space-time parity transformations. For the case of two-soliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of non-linear science. We make a detailed numerical study of the modified NLS potential of the form V = |psi|^(2(2+epsilon)), with epsilon being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasi-integrability concepts recently proposed in the context of modifications of the sine-Gordon model remain valid for perturbations of the NLS model.