The Study Of The Solutions,Multi-component Conservation Laws For Nonlinear Partial Differential Equations

Nonlinear partial differential equation(NLPDEs)are widely used in the field of mathematical physics.Therefore,finding exact solutions and properties of nonlinear partial differential equations is an important topic in the field of mathematical physics.In this paper,we study resonant solutions and rogue wave solutions of the(2+1)-dimensional Caudrey-Dodd-Gibbon equation,exact solutions of the BurgersKorteweg-de-Vries equation,exact solutions of the classical Burgers equation,the selfadjointness and conservation laws of some multi-component integrable systems,mainly for the multi-component Frobenius-type integrable systems and the multi-component Burgers-type integrable systems,and choose the multi-component BKdV integrable systems,multi-component classical Burgers integrable systems,the multi-component MKdV integrable systems to discuss conservation laws.In the first chapter,we mainly introduce research background of exact solutionsself-adjointness,conservation laws for nonlinear partial differential equations,as well as introduce the research methods and contents of the paper.In the second chapter,firstly,the linear superposition principle is introduced,we derive the Hirota bilinear form of(2+1)-dimensional Sawada-Kotera equation by Hirota bilinear method,then with the help of linear superposition principle,the resonant solutions on the real and complex fields are constructed.Then,by using a kind of ansatz method,we construct rogue wave solutions.Finally,the nonlinear dynamical behaviors of the above obtained solutions by 2D and 3D figures,were described.In the third chapter,we mainly use Extended Kudryashov method to construct exact solutions of nonlinear partial differential equations,and the classical Burgers equation is taken as an example.Firstly,we introduce the Extended Kudryashov method,then,by using a kind of ansatz method to construct the solution form of the classical Burgers equation.In the last,we obtain the exact solutions of the classical Burgers equation.In the fourth chapter,we mainly use Extended Kudryashov method and Jacobi Elliptic Function Expansion method to construct exact solutions of nonlinear partial differential equations,and the BKdV equation is taken as an example.Firstly,we construct some exact solutions of the BKdV equation by using the Kudryashov expansion method.Then,we introduce Jacobi Elliptic Function Expansion the method to construct the exact solutions of the BKdV equation.In the fifth chapter,Some multi-component integrable systems are introduced and constructed.These multi-component systems are selected as examples to help us study the self-adjointness of Zn-type equation by means of some new definitions.Then,the conservation laws of these multi-component systems are constructed based on a few symmetries.In the sixth chapter,summarize the research work of this article and provide prospect for future research plans.