Symmetry,Conservation Laws And Solutions Of Two Kinds Of Nonlinear Evolution Equations

The nonlinear evolution equation can be used to describe a large number of nonlinear phenomena in nature,so it has important research value.Solitons and integrable systems is one of the research directions of nonlinear evolution equations,this direction mainly studies the solutions and properties of nonlinear evolution equations,including soliton solutions,rational solutions,integrability,symmetry,Hamiltonian structure,conservation law of nonlinear evolution equations,etc.This thesis mainly studies the exact solution,symmetry and conservation law of the nonlinear evolution equation.The contents are as follows:1.The consistent Riccati expansion(CRE)method is used to prove the CRE solvable property of the modified coupled KdV equation,and three groups of interaction solutions of the modified coupled KdV equation are acquired by using this property.And the corresponding waveforms of the equation can be drawn with Maple.2.The residue symmetries of the modified Broer-Kaup-Kupershmidt(mBKK)equation are constructed according to the Painlev'e truncated expansion method.By localizing the residue symmetries,the corresponding finite symmetric transformations are obtained.Then,the consistent Riccati expansion(CRE)method is proved to be CRE solvable of the modified Broer-Kaup-Kupershmidt(mBKK)equation.By using this property,the interaction solutions of the equation are obtained,and the corresponding waveforms are drawn with Maple.3.The Lie symmetries of the modified Broer-Kaup-Kupershmidt(mBKK)equation are obtained with the method of Lie group,and also the infinite conservation laws of that equation are derived by using the adjoint equation method.