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Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics
American Journal of Applied Mathematics
Volume 3, Issue 3, June 2015, Pages: 100-105
Received: Apr. 6, 2015; Accepted: Apr. 18, 2015; Published: Apr. 29, 2015
Author
S. M. Rayhanul Islam, Department of Mathematics, Pabna University of Science and Technology, Pabna, Bangladesh
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Abstract
In this article, we construct the traveling wave solutions involving parameters of nonlinear evolutions equations via the Benney-Luke equation using the exp(-Φ(ξ))-expansion method. The traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The proposed method is direct, concise elementary and effective and can be used for many other nonlinear evolutions equations.
Keywords
Exp(-Φ(ξ))-Expansion Method, Benney-Luke Equation, Nonlinear Evolution Equations, Traveling Wave Solution
S. M. Rayhanul Islam, Applications of the exp(-Φ(ξ))-Expansion Method to Find Exact Traveling Wave Solutions of the Benney-Luke Equation in Mathematical Physics, American Journal of Applied Mathematics. Vol. 3, No. 3, 2015, pp. 100-105. doi: 10.11648/j.ajam.20150303.14
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