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

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