Modified non-linear Schrödinger models, \cal C\cal P_s\cal T_d symmetry, dark solitons and infinite towers of anomalous charges

2021/02/14 by Blas, H., Maguiña, M. Cerna, Santos, L. F. dos
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2102.07190

Abstract

Some modified (defocusing) non-linear Schrödinger models (MNLS) possess infinite towers of anomalous conservation laws with asymptotically conserved charges. The so-called anomalies of the quasi-conservation laws vanish upon space-time integration for a special \cal C\cal P_s\cal T_d symmetric field configurations. We verify numerically the degree of modifications of the charges around the dark-soliton interaction regions by computing numerically some representative anomalies related to lowest order quasi-conservation laws of the non-integrable cubic-quintic NLS model as a modified (defocusing) NLS model. This modification depends on the parameter ε, such that the standard NLS is recovered for ε=0. Here we present the numerical simulations for small values of |ε|, and show that the collision of two dark solitons are elastic. The NLS-type equations are quite ubiquitous in several areas of non-linear science.

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