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

Entropy

Sheng Zhang¹  Jiahong Li²  Yingying Zhou²  Ignazio Licata² 

[1] id="af1-entropy-17-03182">School of Mathematics and Physics, Bohai University, 19 Keji Road, New Songshan District, Jinzhou 121013, China

关键词: exp-function method;    exponential function ansätz;    non-linear lattice equation;    exact solution;    mKdV lattice equation;   

DOI  :  10.3390/e17053182

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland