T T ¯ $$ T\overline{T} $$ deformations of non-relativistic models

Abstract

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

Keywords

• Integrable Field Theories
• Field Theories in Lower Dimensions