Analytic Investigation Of The Symbolic Computation On The Nonlinear Equations

For the past decades,nonlinear phenomena in fluids,nonlinear opties,biology,condensed matter physics and plasma physic are one of research hot areas in physics.People study those nonlinear phenomena through the nonlinear evolution equations(NLEEs)and their rational solutions.There exist some solutions for the NLEEs,such as the soliton,rogue-wave,lump and breather-wave solutions.With the symbolic computation,those solutions are analytical studied.The main research contents of this dissertation are as follows:(1)The(3+1)-dimensional variable-coefficient Zakharov-Kuznetsov equation is investigated.Via the rational transformation,the equation is transformed to the bilinear forms.One-,two-and three-soliton solutions for the equation are derived.Based on those solutions,the propagation of the one soliton and the collisions between the two solitons and three solitons are graphically analyzed.(2)The(3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation is studied.Under the logarithmic trans-formation,the bilinear forms,lump and breather solutions of the equation are derived.Based on those solutions,effects of the variable coefficients on the propagation of the lump,the amplitude and period of the breather wave are analyzed.(3)The B-typed Kadomtsev-Petviashvili equation is investigated.We construct the lump,breather-wave,rogue-wave and travelling solu-tions for the equation.Fusion and fission interactions between the lump and soliton are graphically discussed.During the interaction between the interaction between the lump wave and two kink waves,a rogue wave generates at one kink wave and merges into another one.Breather waves and rouge waves are respectively displayed,where the rouge waves come from the extreme behaviour of the breather waves.(4)Investigation is carried out on the(3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation.Under the integrable con-ditions,the lump,lump-soliton and rogue-soliton solutions are obtained.The effects of the nonlinear,dispersed and perturbed coefficients on the propagation of the lump and soliton are analyzed.Fission and fusion phenomena for the lump and soliton are discussed.