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arXiv · 2102.12435

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

Chantelle Esper·Sergey Frolov
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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.

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Chantelle Esper, Sergey Frolov. 2021-02-24. $T\overline{T}$ Deformations of nonrelativistic models. https://doi.org/10.1007/jhep06(2021)101

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