The Exact Solutions And The Interaction Dynamics Behavior Of Several Classes Of Nonlinear Soliton Equations

As an important theory in nonlinear science,soliton has been the focus of researchers.The exact soliton solutions of nonlinear evolution equations,which can help people to understand the relationship between the amount of physical interior,have attracted researchers' attention.In view of the specificity of nonlinear evolution equations and the limitations of solving methods,seeking exact solutions of nonlinear evolution equations is still a difficult and important research topic.In this thesis,kinds of nonlinear soliton equations are solved by using several methods,the main contents of this thesis are as follows:1.Lump solitons are obtained from(2+1)-dimensional CDGKS equation and(2+1)-dimensional Ito equation by using a direct method,which is based on Hirota bilinear form of the equations that have special solutions of quadratic function.The general formula of coordinates of the vertex and the amplitude of lump solitons are given.It shows that the direct method is a powerful means to seek lump solutions for nonlinear soliton equations when it combined with the Hirota bilinear method.2.We gained a new direct method by changing the expression of solutions in the original direct method.Interaction solutions are obtained from(2+1)-dimensional Ito equation.The completely non-elastic interaction between a lump and a stripe of the equation is presented,which shows a lump soliton is swallowed by a stripe soliton.The dynamical character shows in this work enriches the variety of the dynamics of higher dimensional nonlinear wave field.3.By changing the expression of solutions in the original direct method,we gained another new direct method.Interaction solutions are obtained from(2+1)-dimensional BLMP equation and(3+1)-dimensional nonlinear evolution equation by using the direct method.The interaction solutions of the two equations presented that a lump appear from a soliton wave and relatively moving between the two sides of the soliton wave and swallowed by it later,which are the completely non-elastic interactions that rare to see.It shows that a lump relatively moving from the state of been swallowed by one side of the soliton wave(a kinky wave or another solitary wave),and separate slowly from this side of the soliton wave,after reaching the maximum separation at t(28)0,the lump gradually walks upon the other side of the soliton wave and finally swallowed by the other side.The dynamical character shows in this work enriches the variety of the dynamics of higher dimensional nonlinear wave field and might be helpful to understand the propagation processes for nonlinear waves in fluid mechanics.