Application Of Hirota Method To The Two Soliton Equations

In this paper, our aim is mainly focused on applying Hirota bilinear method to the (3+1)-dimensional KdV equation with self-consistent sources and the non-isospectral KdV equation. First, by introducing logarithm transformation, the nonlinear equations are transformed into bilinear forms. Second, we study the bilinear equation. In chapter 3, we construct the new type and mixed type (3+1)-dimensional KdV equation by applying the source generation procedure and give the Backlund transformation for the new type (3+1)-dimensional KdV equation. In chapter 4, we derive the Backlund transformation for the non-isospectral KdV equation by using the exchange formulas. Then, we give the Gramm-type solution for the non-isospectral KdV equation.