Study On Conservation Laws And Solutions Of Several Classes Of Fractional Partial Differential Equations

In modern natural sciences,nonlinear science runs through mathematical sciences,life sciences,and earth sciences,and has become an important frontier of scientific re-search.Solitary waves are one of the important concepts that promote the development of nonlinear science.Recently,solitary waves have been highly valued by marine schol-ars and meteorologists.In this paper,we use the semi-inverse method,Euler-Lagrange equation,Agrawal method to construct several kinds of fractional Rossby solitary wave models,and use Lie symmetric method to study the symmetry and conservation laws,and through the simplified Hirota bilinear transformation Methods,residual power series(RPS)method and meshless radial basis(RBF)function method give analytical solutions and numerical solutions.This paper mainly studies three kinds of fractional equation-s:(2+1)dimensional ZK-mZK-BBM equation,generalized(3+1)dimensional Camassa-Holm-Kadomtsev-Petviashvili equation,coupled(3+1)dimensional Navier-Stokes equa-tions,the main contents are as follows:1)First,with the help of the semi-inverse method,Euler-Lagrange equation,Agrawal method,the Lagrangian quantity of the equation is given,and the fractional derivative in the sense of Riemann-Liouville fractional derivative is used instead of Lagrangian.In the classical derivative,the fractional form of several kinds of equations is derived by means of the fractional variation principle.2)Secondly,the symmetry of fractional equations is studied by classical Lie symmetry method.At the same time,based on the new conservation theory,the conservation law of fractional equations is constructed.3)Then the analytic solutions and numerical solutions of the fractional equation are given by the simplified Hirota bilinear transformation method,the residual power series(RPS)method and the meshless radial basis(RBF)function method,and the corresponding error analysis is done.Through the study of different fractional Rossby wave models,more specific nonlinear wave phenomena are foundFinally:All the research in this paper is summarized,and new problems to be studied in the future are proposed...