Applications Of Hirota Bilinear Method To Two Soliton Equations

In this thesis, our aim is mainly focused on applying Hirota bilinear method to the study of a new complex generalization of Hirota-Satsuma coupled KdV equation and a (3+1)-dimensional nonlinear evolution equation. Firstly, by introducing logarithm transformation and rational transformation, the complex generalization of Hirota-Satsuma coupled KdV equation is transformed into bilinear forms and N-soliton solution of the equation is derived by a perturbation method. Then, a Backlund transformation in bilinear forms, Grammian determinant solutions and a new coupled system of a (3+1)-dimensional nonlinear evolution equation are obtained with the aid of the bilinear form of the equation and Hirota-Ohta's pfaffianizataion procedure. Moreover, Gramm-type pfaffian solutions to the coupled system have been given.