Analytic Solution of Nonlinear Partial Differential Equations

Abstract

In this article, we show the Hirota direct method to find exact solutions of nonlinear partial differential equations. These solutions are call ‘soliton solution’. The Hirota direct method is the most famous one method which can construct multi-soliton solutions. And the Hirota method has four processes. The importance process is transforming nonlinear partial differential equations to Hirota bilinear form that can write in polynomial of -operator. We have example of KdV equation for more understanding in the transforming nonlinear equations to bilinear form and find soliton solutions of this equation that we can find to three-soliton solutions.