Hirota method for nonlinear evalution equations

In the first chapter of this thesis, a brief historical development of Partial Differantial Equations is given. In the second chapter, after giving information regarding the KdV equation, the given approaches from past to today about Hirota bilinear method and evaluation equations are analyzed based on historical progress. In the third chapter, the definitions, theorems and some examples for Partial Differantial Equations are given. The fourth chapter is analyzed as two parts. In the first part, after giving information about soliton and soliton interaction, a solution is sought for the KdV equation. In the second part, after we transform the KdV equation, Sawada-Kotera equation, Bousinesq equation and the Kadomtsev-Petviashivili equation into the Hirota bilinear form, Hirota's direct method is applied to the KdV equation, Sawada-Kotera equation, Bousinesq equation and the Kadomtsev-Petviashivili equations in order to have multi-soliton solutions for these equations.