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An algebraic method exactly solving two high-dimensional nonlinear evolution equations. (English) Zbl 1069.35065
Summary: An algebraic method is applied to construct soliton solutions, doubly periodic solutions and a range of other solutions of physical interest for two high-dimensional nonlinear evolution equations. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the solutions at a certain limit condition. Compared with most existing tanh methods, the proposed method gives new and more general solutions. More importantly, the method provides a guideline to classify the various types of the solutions according to some parameters.
MSC:
35Q51Soliton-like equations
37K40Soliton theory, asymptotic behavior of solutions
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