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We consider $lambdaphi^{4}$ kink and sine-Gordon soliton in the presence of a minimal length uncertainty proportional to the Planck length. The modified Hamiltonian contains an extra term proportional to $p^4$ and the generalized Schrodinger equation is expressed as a forth-order differential equation in quasiposition space. We obtain the modified energy spectrum for the discrete states and compare our results with 1-loop resummed and Hartree approximations for the quantum fluctuations. We finally find some lower bounds for the deformations parameter so that the effects of the minimal length have the dominant role.
We study kink-antikink collisions in a model which interpolates smoothly between the completely integrable sine-Gordon theory, the $phi^4$ model, and a $phi^6$-like model with three degenerate vacua. We find a rich variety of behaviours, including in
The perturbed conformal field theories corresponding to the massive Symmetric Space sine-Gordon soliton theories are identified by calculating the central charge of the unperturbed conformal field theory and the conformal dimension of the perturbatio
Our principal focus in the present work is on one-dimensional kink-antikink and two-dimensional kink-antikink stripe interactions in the sine-Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an anti
Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell containing an a
Two series of integrable theories are constructed which have soliton solutions and can be thought of as generalizations of the sine-Gordon theory. They exhibit internal symmetries and can be described as gauged WZW theories with a potential term. The spectrum of massive states is determined.