In this paper we show new exact solutions for a type of generalized sine-Gordon equation which is obtained by constructing a Lagrange function for a dynamical coupled system of oscillators. We convert it into a nonlinear system by perturbing the potential energy from a point of view of an approach proposed by Fermi [1].

In this paper, based on the generalized Jacobi elliptic function expansion method,we obtain abundant new complex doubly periodic solutions of the double Sine-Gordon equation (DSGE), which are degenerated to solitary wave solutions and triangle function solutions in the limit cases,showing that this new method is more powerful to seek exact solutions of nonlinear partial differential equations i...

In this paper we research the exact solutions for a sort of new Sine-Gordon equation. By using the tanh method and a variable separated ordinary difference method, we get some new exact travelling wave solutions, among which there are two new noncontinuous wave solutions.

We study the breather collisions in a weakly discrete sine-Gordon equation and reveal a new mechanism of fractal soliton scattering. We demonstrate how this new mechanism manifests itself in the dynamics of cold soliton gas.r 2002 Elsevier Science B.V. All rights reserved.

In this paper, we apply the modified homotopy perturbation method based on the Taylor series for solving the initial value problems of the two dimensional sine-Gordon equation. Due to the proposed modification , the approximate solution obtained is in accordance with the exact solution greatly. Numerical examples are presented to show its efficiency.

The exact renormalisation group equation is studied for a two dimensional theory with exponential interaction and a background charge at infinity. The motivation for studying this interaction is the flow between unitary minimal models perturbed by Φ(1,3), and their realisation in terms of a quantum group restricted sine-Gordon model.