The Exact Travelling Wave Solutions For Several Types Of Nonlinear Partial Differential Equations

In this paper, the extended Sinh-Cosh technique and the reductionof order for solving di-erential equations are developed to study several types ofnonlinear partial di-erential equations. The analytical expressions of the exactsolutions for these equations are obtained. The main factors leading to thechange in the physical structures of solutions are highlighted.Chapter 1 focuses on the exact travelling wave solution for a modified cou-pled Boussinesq system. The solution is degenerative to hyperbolic and trigono-metric functions as the modulus m of Jacobi elliptic function tends to 1 and 0,respectively.In Chapters 2, 3, and 4, a technique based on the reduction of order forsolving differential equations has been employed to find exact solutions for threekinds of nonlinear equations. The first is a generalized KdV - mKdV equa-tion with high order nonlinear terms. The second is three types of nonlin-ear Klein - Gordon equations. The third is the modified nonlinear dispersivemK(m,n) equations in higher dimensional spaces. Solutions presented in thisarticle possess various forms including bell type or kink type solitary wave so-lutions, solitons, compactons, periodic solutions, algebraic travelling wave solu-tions, etc. From the author's viewpoints, the results acquired in this article partlyextend the corresponding results provided in previous literature.