New family of sine-Gordon models (original) (raw)

Some properties of deformed Sine Gordon models

2008

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.

A mechanical analog for the double sine-Gordon equation

Physica D: Nonlinear Phenomena, 1985

A mechanical analog for the double sine-Gordon equation is proposed and used to analyze solitary solutions for arbitrary parameter values. The extension of this analog to other equations of the multiple sine-Gordon class is also considered.

The sine-Gordon Model and its Applications

Nonlinear Systems and Complexity, 2014

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.

Soliton Solutions in a Modified Double and Triple Sine-Gordon Models

2016

We modify both the double sine-Gordon (DSG) and triple sine-Gordon (TSG) model in (1,1) dimensions by the addition of an extra kinetic term and a potential term to their Lagrangian density and present a modified DSG (MDSG) and a modified TSG (MTSG) models. We obtain soliton solutions of the presented modified models and find that both of them possesses the same solutions of the unmodified model with some extra conditions imposed on the parameters of the models. We study some properties of the modified models, in particular, we show that the corresponding governing equation has two solutions, a special ones, which are the exact solutions of the unmodified models and a general ones, and these two types of solutions are coincides in our presented models. We end the paper with conclusions and some features and comments.

A study of the solutions of the combined sine–cosine-Gordon equation

Applied Mathematics and Computation, 2009

We have studied the solutions of the combined sine-cosine-Gordon Equation found by Wazwaz (App. Math. Comp. 177, 755 (2006)) using the variable separated ODE method. These solutions can be transformed into a new form. We have derived the relation between the phase of the combined sine-cosine-Gordon equation and the parameter in these solutions. Its applications in physical systems are also discussed.

Exact solutions to the sine-Gordon equation

Journal of Mathematical Physics, 2010

A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable x and the temporal variable t, and they are exponentially asymptotic to integer multiples of 2π as x → ±∞. The solution formulas are expressed explicitly in terms of a real triplet of constant matrices. The method presented is generalizable to other integrable evolution equations where the inverse scattering transform is applied via the use of a Marchenko integral equation. By expressing the kernel of that Marchenko equation as a matrix exponential in terms of the matrix triplet and by exploiting the separability of that kernel, an exact solution formula to the Marchenko equation is derived, yielding various equivalent exact solution formulas for the sine-Gordon equation.

Double sine-Gordon model revisited

NUCLEAR PHYSICS B, 2006

We reconsider the mass spectrum of double sine-Gordon theory where recent semiclassical results called into question the previously accepted picture. We use the Truncated Conformal Space Approach (TCSA) to investigate the claims. We demonstrate that the numerics supports the original results, and strongly disagrees with those obtained from semiclassical soliton form factor techniques. Besides the numerical analysis, we also discuss the underlying theoretical arguments. *

Topological defect solutions in new families of sine-Gordon models

We study a new family of models of the sine-Gordon type, starting from the sine-Gordon model, including the double sine-Gordon, the triple one, and so on. The models appears as deformations of the starting model, with the deformation controlled by two parameters, one very small, used to control a linear expansion on it, and the other, which specifies the particular model in the family of models. We investigate the presence of topological defects, showing how the solutions can be constructed explicitly from the topological defects of the sine-Gordon model itself. In particular, we delve into the double sine-Gordon model in a braneworld scenario with a single extra dimension of infinite extent, showing that a stable gravity scenario is admissible. Also, we briefly show that the deformation procedure can be used iteratively, leading to a diversity of possibilities to construct families of models of the sine-Gordon type.

Perturbation theory for the double sine-Gordon equation

Wave Motion, 2005

This paper presents the perturbation theory for the double-sine-Gordon equation. We received the system of differential equations that shows the soliton parameters modification under perturbation's influence. In particular case λ = 0 the results of the research transform into well-known perturbation theory for the sine-Gordon equation.