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Math. Comput. Appl. 2010, 15(5), 910-923; doi:10.3390/mca15050910

Variational Approach to Solitary Solutions Using Jacobi-Elliptic Functions

Economical Mathematics Office, Department of Economics and Management Shanghai University of Political Science and Law, Shanghai 201701, China
Received: 31 December 2010 / Accepted: 31 December 2010 / Published: 31 December 2010
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Abstract

Partial differential equations are transformed into ordinary differential equations, and a variational formulation is then established. The trial function is chosen using Jacobi-elliptic function with some unknown parameters similar to the exp-function method. Various approximate solitary solutions are obtained when making the obtained variational principle stationary with respect to each unknown parameter in the trial-function. The coupled Zakharov-Kuznetsov equations are used as an example to elucidate the solution procedure.
Keywords: Variational theory; semi-inverse method; solitary solution; exp-function method; Jacobi-elliptic function Variational theory; semi-inverse method; solitary solution; exp-function method; Jacobi-elliptic function
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Wu, Y. Variational Approach to Solitary Solutions Using Jacobi-Elliptic Functions. Math. Comput. Appl. 2010, 15, 910-923.

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