Soliton solutions of some partial differential equations with dispersion term

SOLITON SOLUTIONS OF SOME PARTIAL DIFFERENTIAL EQUATIONS WITH DISPERSION TERM This study has been probed in five sections. In the first chapter, the aim of this study has been explained. Some fundamental concepts which are going to be used in the next chapters have been presented. In the second chapter, some information about the Generalized KdV and NLS equations has been given and then the previous studies about these equations have been mentioned. Moreover, some information about soliton, compacton and optic soliton concepts have been presented. In the third chapter, Jacobi elliptic functions have been explained. Soliton and compacton solutions of K(n,n) equation, K(m,n) equation with t-dependent coefficients and generalized NLS equation have been obtained. In the fourth chapter, some fundamental concepts as well as the classical finite difference methods have been presented. Numerical solutions of K(2,3) equation have been obtained using finite difference method. Moreover, in this chapter, the stability analysis of the finite difference approximation used in the thesis has been investigated. In the fifth chapter, the results have been evaluated.