Infinitely Many Elliptic Solutions to a Simple Equation and Applications
Based on auxiliary equation method and Bäcklund transformations, we present an idea to find infinitely many Weierstrass and Jacobi elliptic function solutions to some nonlinear problems. First, we give some nonlinear iterated formulae of solutions and some elliptic function solutions to a simple au...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/582532 |
| Summary: | Based on auxiliary equation method and Bäcklund transformations, we present an idea to find
infinitely many Weierstrass and Jacobi elliptic function solutions to some nonlinear problems.
First, we give some nonlinear iterated formulae of solutions and some elliptic function solutions
to a simple auxiliary equation, which results in infinitely many Weierstrass and Jacobi elliptic
function solutions of the simple equation. Then applying auxiliary equation method to some
nonlinear 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 differential
equations. |
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| ISSN: | 1085-3375 1687-0409 |