Multi-wave Interaction Solutions Of Nonlinear Partial Differential Equations On The Periodic Background

In nonlinear physics,complex nonlinear physical systems are often simplified into nonlinear partial differential equations to study,and the relationship between physical quantities is explained by the exact solutions and mixed solutions of these equations.In this thesis,several kinds of nonlinear partial differential equations are taken as the research objects.The main contents and the related methods of this thesis are as follows(1)The rogue periodic wave solutions(rogue wave solution on the background of Jacobian elliptic dn and cn periodic waves)of AB system and(2+1)-dimensional complex modified Korteweg-de Vries(CMKdV)equation are studied by combining the nonlinear of Lax pair and Darboux transformation(DT).Under the linear stability analysis,it is revealed that modulation instability is the condition for the existence of rogue waves.(2)Based on the spectral problem in KN system,the N-fold Darboux transformation of TOFKN equation is constructed.By using Taylor series expansion method and improved generalized Darboux transformation(GDT)method,the breather solution,rogue wave solution and mixed solution of TOFKN equation on the periodic background are constructed.(3)Based on the Hirota bilinear equation and the long-wave limit method,the N-kink solution,L-breather solution and K-order lump solution of the(2+1)-dimensional Caudrey-Dodd-Gabbon-Kotera-Sawada(CDGKS)equation are derived.Construct appropriate auxiliary functions,the mixed solutions of the above three solutions are obtained by combining the long wave limit or taking complex conjugate parameters.With the change of time,each wave in the mixed wave will have collides elastically.