Research On Several Kinds Of Rossby Solitary Wave Fractional Order Models And Their Properties

Rossby waves are extremely important from both dynamic meteorology and physical ocean perspectives.Many of the problems of nonlinear atmospheric and ocean dynamics can be attributed to the study of Rossby solitary wave evolution.In this paper,the multi-scale analysis method,perturbation method,semi-inverse method,variational method and Euler-Lagrangian equation are used to construct the fractional-order model under different conditions to describe the propagation process of Rossby solitary waves.Different methods are used to obtain the exact solution of the model.Through numerical simulation,the influence of the fractional order on the solution and the intrinsic relationship between the fractional order and the actual nonlinear phenomena are observedFirstly,starting from the quasi-ground vortex equation with dissipative effect under the action of complete Coriolis force in the stratified fluid,using the perturbation method and multi-scale analysis method,the Boussinesq equation with integer order dissipation is obtained.In the semi-anti-method,the Boussinesq equation with time fractional dissipa-tion is obtained with the help of variational method and Euler-Lagrangian equation.The conservation law is discussed by Lie group analysis.The exact solution of the equation is obtained by the improved(G'/G)method,finally,considering the influence of dissipa-tion,the approximate solution of the equation is obtained by the new iterative method Analyze the effect of fractional order on the solutionThen,considering the dimensionless equation of the basic dynamics of atmospher-ic motion,based on the similar method,we first obtain the integer-order nonlinear Schrodinger equation,and on this basis we obtain the fractional nonlinear Schrodinger equation is discussed in depth by the Lie group analysis method.The exact solution of the above equation is obtained by using the exp(—?(?))method.The intrinsic difference between the fractional order and the nonlinear phenomenon of the Rossby solitary wave is compared.contactFinally,based on the basic dynamic equation of baroclinic atmosphere,a similar method is used to obtain the integer-order BO equation,and then the fractional-order BO equation is derived.Using the Hirota bilinear method,the multi-particle solution of the above equation is obtained,and the interaction between particles is discussed.Consider the influence of fractional order on wave-wave interaction and its propagation law.By comparing the effect diagrams used to describe the fractional-order models of different Rossby waves,we find that the influence of the fractional order changes on nonlinear phenomena is huge,which deserves further study.