2008/07/17 by Akmaral Alibek, Alibek, Akmaral, Ratbay Myrzakulov +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.0807.2715
arxiv created 2008/07/17 · openalex publication_date 2008/07/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study some properties of the deformed Sine Gordon models. These models, presented by Bazeia et al, are natural generalisations of the Sine Gordon models in (1+1) dimensions. There are two classes of them, each dependent on a parameter n. For special values of this parameter the models reduce to the Sine Gordon one; for other values of n they can be considered as generalisations of this model. The models are topological and possess one kink solutions. Here we investigate the existence of other solutions of these models - such as breathers. The work is numerical and we find that the breathers, as such, probably do not exist. However, we show that some of these models, namely, the n = 1 of the first class possess breather-like solutions which are quasi-stable; ie these quasi-breathers exist for long periods of time (thousands of periods of oscillations). These results are found to be independent of the discretisation used in the numerical part of our work.