By studying the internal Riemannian geometry of the surfaces of constant negative scalar curvature, we obtain a natural map between the Liouville and the sine–Gordon equations. First, considering isometric immersions into the Lobachevskian plane, we obtain an uniform expression for the general (locally defined) solution of both the equations. Second, we prove that there is a Lie– Bäcklund trans...

We have studied the solutions of the combined sine–cosine-Gordon Equation found by Wazwaz [A.M. Wazwaz, Travelling wave solutions for combined and double combined sine-cosine-Gordon equations by the variable separated ODE method, Appl. Math. Comput. 177 (2006) 755] using the variable separated ODE method. These solutions can be transformed into a new form. We have derived the relation between t...

We discuss the relationship between two-dimensional (2D) dilaton gravity models and sine-Gordon-like field theories. We show that there is a one-to-one correspondence between the solutions of 2D dilaton gravity and the solutions of a (two fields) generalization of the sine-Gordon model. In particular, we find a connection between the soliton solutions of the generalized sine-Gordon model and ex...

The School of Computing and Technology at the University of Sunderland teaches a diverse range of programmes to a disparate range of students. This paper will outline and evaluate the specific subjects taught in each module at each level, the applications and methodologies used, and the relationship between modules at different levels. It will also discuss the various assessment methodologies e...

We complete the construction of all the simple graphs with at most 26 vertices and transitive automorphism group. The transitive graphs with up to 19 vertices were earlier constructed by McKay, and the transitive graphs with 24 vertices by Praeger and Royle. Although most of the construction was done by computer, a substantial preparation was necessary. Some of this theory may be on independent...

In this article we will develop some techniques aimed at the strong couplings in two-dimensional wave-Klein-Gordon system. We distinguish roles of different type decay factors and a method which permits us to “exchange” one into other. Then global existence result model problem is established. also give sketch Klein-Gordon-Zakharov system establish associate result.

in this paper, based on sinh-cosh method and sinh-gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.these solutions include jacobi elliptic function solution, soliton solution,trigonometric function solution.

Complete discrimination system for polynomial and direct integral method were discussed systematically. In particularly, we pointed out some mistaken viewpoints. Combining with complete discrimination system for polynomial, direct integral method was developed to become a powerful method and was applied to a lot of nonlinear mathematical physics equations. All single traveling wave solutions to...