https://doi.org/10.1140/epjp/i2014-14192-1
Regular Article
Exact solutions for fifth-order KdV-type equations with time-dependent coefficients using the Kudryashov method
1
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
2
Department of Engineering sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran
* e-mail: mostafa.eslami@umz.ac.ir
** e-mail: mirzazadehs2@guilan.ac.ir
Received:
30
June
2014
Revised:
6
August
2014
Accepted:
8
August
2014
Published online:
11
September
2014
The KdV equation plays an important role in describing motions of long waves in shallow water under gravity, one-dimensional nonlinear lattice, fluid mechanics, quantum mechanics, plasma physics, nonlinear optics and other areas. The KdV equation is a well-known model for the description of nonlinear long internal waves in a fluid stratified by both density and current. The aim of this paper is to present solitary wave solutions of the fifth-order KdV equations with time-dependent coefficients. The Kudryashov method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving high-order nonlinear partial differential equations with time-dependent coefficients in mathematical physics.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2014
