On Rogue Wave In The Kundu-DNLS Equation

In this dissertation, under the guidance of integrable system and by means of computer algebraic system software, reviews the history and development of soliton solution, and introduce the development and research of the DNLS equation, what’s more, we reviews the history and development of rogue waves. At present, there are many ways of solving the exact solutions of derivative nonlinear Schrodinger (DNLS) equation,in this article, by use the Darboux transformation and keep the correspond-ing gauge transformation, the determinant representation of the Darboux transforma-tion of the Kundu-DNLS equation is given. Based on our analysis, by the Darboux transformation, the soliton solutions, positon solutions and breather solutions of the Kundu-DNLS equation are given explicitly. Further, we also construct the rogue wave solutions which are given by using the Taylor expansion of the breather solution. Par-ticularly, these rogue wave solutions possess several free parameters. By choosing the arbitrary constants and arbitrary functions suitably, these rogue waves constitute sev-eral patterns, such as fundamental pattern, triangular pattern, circular pattern.The thesis is arranged as follows:Chapter1. Reviews the history and development of soliton solution; introduce the development and research of the DNLS equation, Further,reviews the history and development of rogue waves.Chapter2. The Darboux transformation and the determinant representation of the Darboux transformation of the Kundu-DNLS equation is given.Chapter3. By the Darboux transformation, the soliton solutions, positon solutions are given explicitly by different seed solutions by the zero solutions.Chapter4. By the no-zero solutions, We also construct the rogue wave solutions which are given by using the Taylor expansion of the breather solution. By choosing the arbitrary constants and arbitrary functions suitably,these rogue waves constitute several patterns, such as fundamental pattern, triangular pattern, circular pattern. Chapter5. Conclusion and discussion.