Study On Rogue Periodic Waves And Hybrid Solutions For Higher-order Nonlinear Equations

In this paper,rogue periodic wave solutions of the higher-order nonlinear wave equations are acquired by using the Darboux transformation and approach of the nonlinearization of spectral problem,and hybrid solutions of the higher-dimensional nonlinear evolution equations are constructed by means of the Hirota bilinear transformation and the long-wave limit approach.The main work is as follows:(1)Using the Jacobi elliptic function expansion method,elliptic function solutions of a generalized fifth-order nonlinear Schr(?)dinger(NLS)equation are gotten.Through the approach of the nonlinearization of spectral problem and then the Darboux transformation method,two kinds of rogue periodic waves for the generalized fifth-order NLS equation which are on Jacobi elliptic functions dn and cn background are gotten.Furthermore,the nonlinear dynamic properties of the rogue periodic wave solutions are shown.(2)Based on the Hirota bilinear method,multi-kink solutions of a(2+1)-dimensional completely generalized Hirota-Satsuma-Ito(cg HSI)equation are obtained.Based on the multi-kink solutions,the higher-order lump solutions and the multi-breather solutions of this equation can be constructed,respectively,by the long-wave limit and selecting the complex conjugate conditions of the parameters.In particular,ten kinds of hybrid solutions consisted of three waves for kink,breather and lump are obtained by classification.Some dynamical behaviors of the solutions obtained are shown by figures.(3)Combining the Hirota bilinear method,the skill of taking complex conjugate of the parameters for multi-soliton solutions and the long-wave limit approach,we drive the multi-soliton solutions,the higher-order breather solutions,the lump solutions and abundant hybrid solutions formed of solitons,breathers and lumps of a(2+1)-dimensional variable coefficient KP equation successively.By some special parameters selection,the periodicity or aperiodicity and rich evolutionary conditions of the solutions obtained are illustrated by diagrams.