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Entropy 2015, 17(5), 3182-3193; doi:10.3390/e17053182

Exact Solutions of Non-Linear Lattice Equations by an Improved Exp-Function Method

School of Mathematics and Physics, Bohai University, 19 Keji Road, New Songshan District, Jinzhou 121013, China
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Academic Editors: Ignazio Licata and Sauro Succi
Received: 9 April 2015 / Revised: 29 April 2015 / Accepted: 30 April 2015 / Published: 13 May 2015
(This article belongs to the Special Issue Non-Linear Lattice)
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Abstract

In this paper, the exp-function method is improved to construct exact solutions of non-linear lattice equations by modifying its exponential function ansätz. The improved method has two advantages. One is that it can solve non-linear lattice equations with variable coefficients, and the other is that it is not necessary to balance the highest order derivative with the highest order nonlinear term in the procedure of determining the exponential function ansätz. To show the advantages of this improved method, a variable-coefficient mKdV lattice equation is considered. As a result, new exact solutions, which include kink-type solutions and bell-kink-type solutions, are obtained. View Full-Text
Keywords: exp-function method; exponential function ansätz; non-linear lattice equation; exact solution; mKdV lattice equation exp-function method; exponential function ansätz; non-linear lattice equation; exact solution; mKdV lattice equation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Zhang, S.; Li, J.; Zhou, Y. Exact Solutions of Non-Linear Lattice Equations by an Improved Exp-Function Method. Entropy 2015, 17, 3182-3193.

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