The evolution of spectral data for nonlinear Klein-Gordon models

TL;DR

This paper explores how breaking integrability affects the conserved quantities in nonlinear Klein-Gordon models, using a deformation of the inverse scattering method to analyze quasi-integrable systems.

Contribution

It introduces a novel approach to study quasi-integrable Klein-Gordon models through a deformed inverse scattering method, extending understanding of integrability breaking.

Findings

Quasi-integrable models retain some integrable properties.

Deformation of inverse scattering method is effective for analysis.

Results shed light on the impact of integrability breaking.

Abstract

We investigate the effect of the breaking of integrability in the integrals of motion of a sine-Gordon-like system. The class of quasi-integrable models, discussed in the literature, inherits some of the integrable properties they are associated with. Our strategy, to investigate the problem through a deformation of the so-called inverse scattering method, has proven to be useful in the discussion of generic nonlinear Klein-Gordon potentials, as well as in particular cases presented here.