Soliton-like behaviour in non-integrable systems

TL;DR

This paper introduces a method to construct stable, soliton-like excitations in non-integrable multicomponent systems by reducing them to effective chiral field theories, enabling the use of multi-soliton solutions from integrable models.

Contribution

The authors develop a general scheme to generate robust, soliton-like excitations in non-integrable systems by reduction to simpler integrable equations, advancing the understanding of localized excitations.

Findings

Constructed soliton-like profiles with minimal radiation in non-integrable systems.

Demonstrated the reduction of complex systems to uncoupled KdV equations for each sound speed.

Showed the evolution of excitations closely resembles true solitons of integrable models.

Abstract

We present a general scheme for constructing robust excitations (soliton-like) in non-integrable multicomponent systems. By robust, we mean localised excitations that propagate with almost constant velocity and which interact cleanly with little to no radiation. We achieve this via a reduction of these complex systems to more familiar effective chiral field-theories using perturbation techniques and the Fredholm alternative. As a specific platform, we consider the generalised multicomponent Nonlinear Schr\"{o}dinger Equations (MNLS) with arbitrary interaction coefficients. This non-integrable system reduces to uncoupled Korteweg-de Vries (KdV) equations, one for each sound speed of the system. This reduction then enables us to exploit the multi-soliton solutions of the KdV equation which in turn leads to the construction of soliton-like profiles for the original non-integrable system. We demonstrate that this powerful technique leads to the coherent evolution of excitations with minimal radiative loss in arbitrary non-integrable systems. These constructed coherent objects for non-integrable systems bear remarkably close resemblance to true solitons of integrable models. Although we use the ubiquitous MNLS system as a platform, our findings are a major step forward towards constructing excitations in generic continuum non-integrable systems.