Infinitely Many Elliptic Solutions to a Simple Equation and Applications | Zendy

Long Wei | Zendy; Yang Wang | Zendy

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Infinitely Many Elliptic Solutions to a Simple Equation and Applications

Author(s) -

Long Wei,

Yang Wang

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/582532

Subject(s) - mathematics , elliptic function , jacobi elliptic functions , simple (philosophy) , iterated function , nonlinear system , elliptic curve , function (biology) , mathematical analysis , elliptic partial differential equation , elliptic integral , quarter period , differential equation , philosophy , physics , epistemology , quantum mechanics , evolutionary biology , biology

Based on auxiliary equation method and Bäcklund transformations, we present an idea to findinfinitely many Weierstrass and Jacobi elliptic function solutions to some nonlinear problems. First, we give some nonlinear iterated formulae of solutions and some elliptic function solutionsto a simple auxiliary equation, which results in infinitely many Weierstrass and Jacobi ellipticfunction solutions of the simple equation. Then applying auxiliary equation method to somenonlinear problems and combining the results with exact solutions of the auxiliary equation,we obtain infinitely many elliptic function solutions to the corresponding nonlinear problems. The employed approach is powerful and can be also applied to solve other nonlinear differentialequations

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