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

Abstract

The light-cone gauge approach to $T\overline{T}$ deformed models is used to derive the $T\overline{T}$ deformed matrix nonlinear Schrödinger equation, the Landau--Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of the $T\overline{T}$ deformed nonlinear Schrödinger 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.

34 pages, many figures. V2: minor corrections. V3: Two new comment sections added, accepted for publication in JHEP

References in corpus (8)

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Cited by in corpus (8)

• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Massive gravity generalization of $T\overline{T}$ deformations
• $T\bar{T}$ flow as characteristic flows
• New classical integrable systems from generalized $T\bar{T}$-deformations
• $T\bar{T}$ deformed soft theorem
• Irrelevant and marginal deformed BMS field theories
• On correlators in $T\bar{T}$-deformed conformal field theories