Modified nonlinear Schrödinger models, 𝒞𝒫s𝒯d invariant N-bright solitons and infinite towers of anomalous charges

Abstract

Modifications of the nonlinear Schrödinger (MNLS) model [Formula: see text] where [Formula: see text] and [Formula: see text], are considered. We show that the MNLS models possess infinite towers of quasi-conservation laws for soliton-type configurations with a special complex conjugation, shifted parity and delayed time reversion ([Formula: see text]) symmetry. Infinite towers of anomalous charges appear even in the standard NLS model for [Formula: see text] invariant [Formula: see text]-bright solitons. The true conserved charges emerge through some kind of anomaly cancellation mechanism. Our analytical results are supported by numerical simulations of two-bright-soliton scatterings with potential [Formula: see text]. Our numerical simulations show the elastic scattering of bright solitons for a wide range of values of the set [Formula: see text] and a variety of amplitudes and relative velocities. The MNLS-type systems are quite ubiquitous, and so, our results may find potential applications in several areas of nonlinear physics, such as Bose–Einstein condensation, superconductivity, soliton turbulence and the triality among gauge theories, integrable models and gravity theories.

Modified AKNS model, Riccati-type pseudo-potential approach and infinite towers of quasi-conservation laws

“…a in (2.51)-(2.52) can be identified, dropping surface terms, to the one for the MNLS model discussed in sec. 3.6 of [13].…”

“…in sec. 3.2 (with n = 2) of the companion paper [13] for the (modified) NLS model provided that the field identifications (2.12) are performed.…”

“…Similarly, this quasi-conservation law corresponds, up to an overall factor 1 4 , to the eq. 3.26 (with n = 1) in the companion paper [13] for the modified NLS model provided that the field identifications (2.12) are performed.…”

“…So, it would be desirable to examine those properties for NLS-type models defined for a complex field with envelope solitons. Some of the mentioned properties have recently been examined for a deformed NLS model in [13] by direct construction of novel quasi-conservation laws starting from the eqs. of motion.…”

“…Remarkably, a new dual system of the Riccati-type pseudo-potential approach is introduced which provides infinite sets of novel anomalous conservation laws. Those quasi-conservation laws encompass, as a subset, the ones obtained by a direct constructive method for the MNLS model in the companion paper [13].…”