Abstract
The light-cone gauge approach to Toverline{T} deformed models is used to derive the Toverline{T} deformed matrix nonlinear Schrödinger equation, the Landau-Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of the Toverline{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 Toverline{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 Toverline{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.
Highlights
There are various connections of T T deformed relativistic models to two-dimensional gravity
Many non-relativistic models, for example the nonlinear Schrödinger (NLS) equation, the Landau-Lifshitz (LL) equation and the Gardner equation which is a combination of the Korteweg-de Vries (KdV) and the modified KdV equation, play important roles in describing various phenomena in nonlinear optics, hydrodynamics, plasma physics and condensed matter physics
The T T deformed Gardner model is more involved because the auxiliary fields appear in the deformed action together with their space derivatives, and it is unlikely that there exists a local deformed action depending only on the physical field
Summary
In a non-relativistic case the seed Lagrangian (2.1) may include total derivative terms which do not change the equations of motion of the seed model but they do change the canonical stress-energy tensor and as a result the Lagrangian and the equations of motion of the deformed model may depend on the total derivative terms. This dependence does not seem to be spurious, and we do not think that it can be undone by a field redefinition
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