We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations can be cast in terms of a Schrödinger-like operators for fluctuations and their spectra are calculated. PACS numbers: 0.350.-z, 11.10.Ef

In Phys. Rev. B 42, 2290 (1990) we used a rigorous projection operator collective variable formalism for nonlinear Klein-Gordon equations to prove the continuum sine-Gordon (SG) equation has a long lived quasimode whose frequency is in the continuum just above the lower phonon band edge with a lifetime . We confirmed the analytic calculations by simulations which agreed very closely with the an...

In this paper classical solutions of the degenerate fifth Painlev\'e equation are classified, which include hierarchies algebraic and expressible in terms Bessel functions. Solutions known to third equation. Two applications these discussed, deriving exact complex sine-Gordon coefficients three-term recurrence relation associated with generalised Charlier polynomials.

Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and ‘‘chaos cascade’’ referring to the embeddings of smaller scale chaos in larger scale chaos. 2003 Elsevier Ltd. All rights reserved.

This paper explores the utility of a discrete singular convolution (DSC) algorithm for the integration of the sine-Gordon equation. The initial values are chosen close to a homoclinic manifold for which previous methods have encountered significant numerical difficulties such as numerically induced spatial and temporal chaos. A number of new initial values are considered, including a case where...