Research On The Symmetries,Conservation Laws And Analytical Solutions To Some Nolinear Differential Equations

In this thesis,we study the symmetry,conservation laws and the analytical solu-tions for several types of nonlinear differential equations.Firstly,the related background and the main work of this thesis are briefly in-troduced.And then,the Lie symmetry method is extended to the Kudryashov-Sinelshchikov equation,which can describe the pressure wave.Its infinitesimal sym-metric vector fields and group invariant solutions are obtained.Based on this,the exact analytical power series solutions of the equation are obtained.In the third and fourth chapters,the symmetric classification analysis of the gen-eralized Korteweg-de Vries-Fischer equation is carried out in detail.And the vector fields of the infinitesimal symmetry for the equation are obtained.on the basis of this,we investigate the self-adjoint properties of the equation.In addition,according to the adjoint equation method and the conservation multiplier direct construction method,we study the conservation laws of the equation systematically.In the fifth and sixth chapters,based on the Hirota bilinear method,the Bell poly-nomials and Riemann theta function are extended to the(3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation result in its bilinear form and analytic solu-tions,which includes soliton solutions and periodic wave solutions.Furthermore,the asymptotic behavior of the periodic wave solutions is studied.We prove that the peri-odic wave solutions can degenerate into soliton solutions under some limit condition,and finally we give a graphical simulation and analysis.Next,based on the integrable discretizations theory,we study the semi-discrete versions and fully discrete version of the Schrodinger-type equation Eckhaus-Kundu equation,giving the soliton solutions and graphic simulation.Finally,we give some summarizes and prospects of this thesis.