Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 39, Issue 10, Pages 2752-2760Publisher
WILEY
DOI: 10.1002/mma.3727
Keywords
KdV equation; RLW equation; TRLW equation; traveling wave; generalized Kudryashov method
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This paper aims to present the generalized Kudryashov method to find the exact traveling wave solutions transmutable to the solitary wave solutions of the ubiquitous unsteady Korteweg-de Vries equation and its two famed alternatives, namely, the regularized long-wave equation and the time regularized long-wave equation. The exact analytic solutions of the studied equations are constructed explicitly in three forms, namely, hyperbolic, trigonometric, and rational function. The validity of our solutions is verified with MAPLE by putting them back into the original equation and found correct. Moreover, it has shown that the generalized Kudryashov method is an easy and reliable technique over the existing methods. Copyright (c) 2016 John Wiley & Sons, Ltd.
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