| There are few absolute linear relationships in the laws of nature,and nonlinear relationships are closer to the nature of the development of things in nature.With the in-depth study of various nonlinear phenomena,nonlinear science has developed rapidly,and promoted the wide application of nonlinear partial differential equation in physics,mechanics and other fields.One of the core problems of nonlinear partial differential equation is to find exact solutions.The rich exact solutions make the model display more intuitive.Therefore,this paper studies two kinds of nonlinear differential equations by using direct integration method and generalized coupled trial equation method,and completes the construction of solutions.The specific research contents are as follows:The first model studies the(2+1)-dimensional generalized coupled nonlinear Schr(?)dinger system with four-wave mixing term.By using the direct integration method and the second order complete discrimination system for polynomials method,four kinds of exact solutions of the coupled system are obtained,including discontinuous periodic solutions,solitary wave solutions,rational function solutions and Jacobi elliptic function solutions.The parameters in the solution of the equation are specifically valued,and the two-dimensional graph and the three-dimensional graph of the mode are drawn by Mathematica.The second model studies the coupled Schr(?)dinger-Kd V system.The generalized coupled trial equation method and the second order complete discrimination system for polynomials method are used to solve the system.A series of exact traveling wave solutions are obtained,including discontinuous periodic solutions,solitary wave solutions and Jacobi elliptic function solutions.In addition,by selecting different parameters for the solutions of the equation,the three-dimensional graphs of the modulus of the solutions are drawn,and the space-time structure of the solutions can be better displayed through these images. |
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