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A simple method in solving high-dimensional nonlinear equations. (Chinese. English summary) Zbl 1340.35297

Summary: High-dimensional nonlinear equations are solved by the trial function method. By introducing transformation and selecting appropriate trial functions, the high-dimensional nonlinear partial differential equations that are hard to be solved by the usual ways can be reduced to a set of algebraic equations, which can be easily solved, and their related coefficients can be easily determined by the undetermined coefficient method. Finally, the analytical solutions to the equations are successfully derived.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C05 Solutions to PDEs in closed form
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