$T\overline{T}$ Deformations of nonrelativistic models

TL;DR

This paper explores how $Tar{T}$ deformations affect nonrelativistic integrable models, deriving deformed equations and analyzing soliton solutions, revealing phenomena like soliton width changes and new solution parameters.

Contribution

It introduces the $Tar{T}$ deformation framework for nonrelativistic models and derives deformed equations with detailed soliton solution analysis, highlighting novel properties.

Findings

Deformed nonlinear Schrödinger and KdV equations derived.

Soliton width can widen or narrow depending on parameters.

Additional solution parameters modify soliton properties.

Abstract

The light-cone gauge approach to $T\overline{T}$ deformed models is used to derive the $T\overline{T}$ deformed matrix nonlinear Schr\"odinger equation, the Landau--Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of the $T\overline{T}$ deformed nonlinear Schr\"odinger and Korteweg--de Vries equations are discussed in detail. The NLS soliton exhibits the recently discussed phenomenon of widening/narrowing width of particles under the $T\overline{T}$ deformation. However, whether the soliton's size is increasing or decreasing depends not only on the sign of the deformation parameter but also on soliton and potential parameters. The $T\overline{T}$ deformed KdV equation admits a one-parameter family of one-soliton solutions in addition to the usual velocity parameter. The extra parameter modifies the properties of the soliton, in particular, it appears in the dispersion relation.