The Solutions For Generalized Complex Modified KdV Equation And The Dynamics Analysis Of Rogue Wave Solutions

In this paper,we investigate the solution and dynamics analysis of rogue wave solution for generalized complex modified Korteweg–de Vries equation which is the 5th-order extended complex modified Korteweg–de Vries(ecmKdV)equation.In the first chapter,we mainly introduce the history and development of the Darboux transformation,soliton,rogue wave,soliton molecule and positon solution.In the second chapter,we construct the Darboux transformation and degenerate Darboux transformation of ecmKdV equation.The connection between new solution and seed solution of ecmKdV equation is generated by Darboux transformation and degenerate Darboux transformation.In the third chapter,taking the zero seed solution,the soliton solution and positon solution of ecmKdV equation can be obtained based on Darboux transformation and degenerate Darboux transformation,respectively.Then,breather solutions,soliton molecules,breather molecules,breather-soliton molecules,soliton molecule-positons and breatherpositons for ecmKdV equation are obtained under the conditions of module resonance and velocity resonance.In the fourth chapter,taking the nonzero seed solution,periodic solutions,rational solutions,rational positon solutions,breather solutions,breather-positon solutions and rogue wave solutions of ecmKdV equation are obtained on the basis of Darboux transformation and degenerate Darboux transformation.In particular,we obtain Kuznetsov-Ma breather and Akhmediev breather solutions which evolve in time direction and space direction,respectively.In the fifth chapter,we consider the dynamics analysis of rogue wave solutions for ecmKdV equation.Under the standard decomposition,the fundamental pattern,triangular pattern and ring pattern of ecmKdV equation are obtained.We analyze the contour lines of rogue wave at different heights and define the length and width of rogue wave by contour line method.We discuss the effect of different parameters on rogue wave solutions.Conclusions and outlooks are given in the sixth chapter.