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