- Journal Home
- Volume 37 - 2024
- Volume 36 - 2023
- Volume 35 - 2022
- Volume 34 - 2021
- Volume 33 - 2020
- Volume 32 - 2019
- Volume 31 - 2018
- Volume 30 - 2017
- Volume 29 - 2016
- Volume 28 - 2015
- Volume 27 - 2014
- Volume 26 - 2013
- Volume 25 - 2012
- Volume 24 - 2011
- Volume 23 - 2010
- Volume 22 - 2009
- Volume 21 - 2008
- Volume 20 - 2007
- Volume 19 - 2006
- Volume 18 - 2005
- Volume 17 - 2004
- Volume 16 - 2003
- Volume 15 - 2002
- Volume 14 - 2001
- Volume 13 - 2000
- Volume 12 - 1999
- Volume 11 - 1998
- Volume 10 - 1997
- Volume 9 - 1996
- Volume 8 - 1995
- Volume 7 - 1994
- Volume 6 - 1993
- Volume 5 - 1992
- Volume 4 - 1991
- Volume 3 - 1990
- Volume 2 - 1989
- Volume 1 - 1988
Solitons and Other Solutions for the Generalized KdV–mKdV Equation with Higher-order Nonlinear Terms
Cited by
Export citation
- BibTex
- RIS
- TXT
@Article{JPDE-29-218,
author = {Zayed , Elsayed M. E. and Al-Nowehy , A. G.},
title = {Solitons and Other Solutions for the Generalized KdV–mKdV Equation with Higher-order Nonlinear Terms},
journal = {Journal of Partial Differential Equations},
year = {2016},
volume = {29},
number = {3},
pages = {218--245},
abstract = { The generalized sub-ODEmethod, the rational (G' ⁄ G)-expansionmethod, the exp-function method and the sine-cosine method are applied for constructing many traveling wave solutions of nonlinear partial differential equations (PDEs). Some illustrative equations are investigated by these methods and many hyperbolic, trigonometric and rational function solutions are found. We apply these methods to obtain the exact solutions for the generalized KdV-mKdV (GKdV-mKdV) equation with higher-order nonlinear terms. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics. We compare between the results yielding from these methods. Also, a comparison between our new results in this paper and the well-known results are given.},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v29.n3.5},
url = {http://global-sci.org/intro/article_detail/jpde/5090.html}
}
TY - JOUR
T1 - Solitons and Other Solutions for the Generalized KdV–mKdV Equation with Higher-order Nonlinear Terms
AU - Zayed , Elsayed M. E.
AU - Al-Nowehy , A. G.
JO - Journal of Partial Differential Equations
VL - 3
SP - 218
EP - 245
PY - 2016
DA - 2016/09
SN - 29
DO - http://doi.org/10.4208/jpde.v29.n3.5
UR - https://global-sci.org/intro/article_detail/jpde/5090.html
KW - Generalized sub-ODE method
KW - rational (G' ⁄ G)-expansion method
KW - exp-function method
KW - sine-cosine method
KW - generalized KdV-mKdV equation with higher-order nonlinear terms
KW - exact solutions
KW - solitary wave solutions
AB - The generalized sub-ODEmethod, the rational (G' ⁄ G)-expansionmethod, the exp-function method and the sine-cosine method are applied for constructing many traveling wave solutions of nonlinear partial differential equations (PDEs). Some illustrative equations are investigated by these methods and many hyperbolic, trigonometric and rational function solutions are found. We apply these methods to obtain the exact solutions for the generalized KdV-mKdV (GKdV-mKdV) equation with higher-order nonlinear terms. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics. We compare between the results yielding from these methods. Also, a comparison between our new results in this paper and the well-known results are given.
Elsayed M. E. Zayed & A. G. Al-Nowehy. (2019). Solitons and Other Solutions for the Generalized KdV–mKdV Equation with Higher-order Nonlinear Terms.
Journal of Partial Differential Equations. 29 (3).
218-245.
doi:10.4208/jpde.v29.n3.5
Copy to clipboard