Generalized sine-Gordon solitons

TL;DR

This paper develops analytical self-dual soliton solutions in (1+1) dimensions for generalized sine-Gordon models with non-canonical kinetic terms, revealing how soliton properties change with non-linearity.

Contribution

It introduces a projection method to construct solitons in generalized sine-Gordon models, extending the deformation method for a specific class of k-field models.

Findings

Soliton solutions reduce to Klein-Gordon kink and lump in the canonical limit.

Increasing non-linearity modifies potentials and soliton topology.

The method generalizes existing deformation techniques for k-field models.

Abstract

In this paper we construct analytical self-dual soliton solutions in (1+1) dimensions for two families of models which can be seen as generalizations of the sine-Gordon system but where the kinetic term is non-canonical. For that purpose we use a projection method applied to the Sine-Gordon soliton. We focus our attention on the wall and lump-like soliton solutions of these k-field models. These solutions and their potentials reduce to those of the Klein-Gordon kink and the standard lump for the case of canonical kinetic term. As we increase the non-linearity on the kinetic term the corresponding potentials get modified and the nature of the soliton may change, in particular, undergoing a topology modification. The procedure constructed here is shown to be a sort of generalization of the deformation method for a specific class of k-field models.