We determine the quantized function algebras associated with various examples of generalized sine-Gordon models. These are quadratic algebras of the general Freidel-Maillet type, the classical limits of which reproduce the lattice Poisson algebra recently obtained for these models defined by a gauged Wess-Zumino-Witten action plus an integrable potential. More specifically, we argue based on th...

We consider an integrable generalization of the sine-Gordon (sG) equation that was earlier derived by one of the authors using bi-Hamiltonian methods. This equation is related to the sG equation in the same way that the Camassa-Holm equation is related to the KdV equation. In this paper we: (a) Derive a Lax pair. (b) Use the Lax pair to solve the initial value problem on the line. (c) Analyze s...

Generalized Cauchy matrix approach is used to investigate a discrete negative Ablowitz–Kaup–Newell–Segur (AKNS) equation. Several kinds of solutions more than multi-soliton this equation are derived by solving determining set. Furthermore, applying an appropriate continuum limit we obtain semidiscrete AKNS and after second derive the nonlinear The reductions discrete, semi-discrete continuous s...

In this paper, the Exp-function method is used to obtain generalized travelling wave solutions with free parameters of the MKdV-sine-Gordon and Boussinesq-double sine-Gordon equations. It is shown that the Exp-function method, with the help of any symbolic computation packages, provides an effective mathematical tool for nonlinear evolution equations arising in mathematical physics.

With the help of computer symbolic computation software e.g., Maple , abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equati...

We report on the possibility of unidirectional motion of a topological soliton in a dissipative AC-driven sine-Gordon equation. This motion is due to breaking of certain space-time symmetries. It can be achieved by the proper choice of the potential or the AC force. We formulate the necessary symmetry conditions for the AC force and confirm them with the first order perturbation theory and nume...