Soliton And Rogue Wave Solutions Of The Hirota Type Equation

In this paper, the rogue wave solutions of two kinds of nonlinear Hirota typeequation are investigated by diferent methods. The determinant representation of then-fold Darboux transformation of the Hirota equation is given. Based on the Darbouxtransformation, the1-soliton,2-soliton and breather solutions are obtained explicitlyfrom zero and nonzero seed solutions respectively. Further, the first order rogue wavesare given by the Taylor expansion of this breather solutions. The rogue wave hasseveral parameters, which provides a systematic way to tune experimentally the roguewaves by choosing diferent values for them.Then, the rogue wave solution of a variable coefcient nonlinear Hirota equationcan be given from the rogue waves of this constant coefcient nonlinear Hirota equationby a transformation which maps the variable coefcient Hirota equation into the Hirotaequation. This rogue wave contains two arbitrary functions, therefore, we can choosediferent control functions to realize the rogue wave management.The chapters and contents are follows:The first chapter introduces the history of solitons and usual methods of solvingnonlinear evolution equations and progress of the research of rogue waves. Then thischapter introduces the theory of Darboux transformation and gives some examples ofsolitons.The second chapter discusses the Lax pair, Darboux transformation and soliton,breather, rogue wave solutions of the Hirota equation in detail. Further, some roguewaves of other equations are given.The third chapter discusses a transformation which maps a variable coefcientequation into the constant coefcient Hirota equation, the corresponding theorem isgiven.The fourth chapter gives the rogue wave solutions of the variable coefcient Hirotaequation according to the conclusions of the second and third chapters, and discusses the evolution of rogue waves.The fifth chapter gives some conclusions and discussions.