New Weierstrass Semi-rational Expansion Method to Doubly Periodic Solutions of Soliton Equations |
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Authors: | YAN Zhen-Ya |
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Institution: | Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, the Chinese Academy of Sciences, Beijing 100080, China |
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Abstract: | Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem
solving soliton equations into
another one solving the corresponding set of nonlinear algebraic equations.
With the aid of Maple, we choose the modified KdV equation,
(2+1)-dimensional KP equation,
and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm.
As a consequence, many types of new doubly periodic solutions are obtained
in terms of the Weierstrass elliptic function. Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple
limits of doubly periodic solutions. |
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Keywords: | soliton equations Weierstrass elliptic function doubly periodic solution symbolic computation |
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