The Two - Variable (G/ G ,) (1/ G) - Expansion Method for Solving Nonlinear Dynamics of Microtubles - A New Model
The ( )-expansion method; Nonlinear dynamics of microtubules; Traveling wave solutions; Solitary wave solutions; Kink-anti kink shaped
Abstract
In this paper, we employ the ( )-expansion method to find the exact traveling wave solutions involving parameters of nonlinear dynamics of microtubulesa New Model . When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the proposed method provides a more powerful mathematical tool for constructing exact traveling wave solutions for many other nonlinear evolution equations.
Downloads
How to Cite
References
W Maliet (1992) Solitary wave solutions of nonlinear wave equations. 60(7), 650-654.
Willy Malfliet, Willy Hereman (1996) The tanh method: I. Exact solutions of nonlinear evolution and wave equations. 54(6), 563-568.
A Wazwaz (2004) The tanh method for travelling wave solutions of nonlinear equations. 154, 714-723.
S El-Wakil, M Abdou (2007) New exact travelling wave solutions using modified extended tanh-function method. 31(4), 840-852.
E Fan (2000) Extended tanh-function method and its applications to nonlinear equations. 277, 212-218.
A Mahmoud, Abdelrahman, H Emad, M Zahran Mostafa, Khater (2015) Exact Traveling Wave Solutions for Modi_ed Liouville Equation Arising in Mathematical Physics and Biology. 112(12).
A Wazwaz (2005) Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method. 50(10-12), 1685-1696.
A-M Wazwaz (2004) A sine-cosine method for handlingnonlinear wave equations. 40(5-6), 499-508.
Chuntao Yan (1996) A simple transformation for nonlinear waves. 224(1-2), 77-84.
Engui Fan, Hongqing Zhang (1998) A note on the homogeneous balance method. 246(5), 403-406.
M Wang (1996) Exct solutions for a compound KdV-Burgers equation. 213, 279-287.
H Emad, Zahran, M Mostafa, Khater (2014) The modified simple equation method and its applications for solving some nonlinear evolutions equations in mathematical physics. 64(5).
Yu-Jie Ren, Hong-Qing Zhang (2006) A generalized F-expansion method to find abundant families of Jacobi Elliptic Function solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation. 27(4), 959-979.
Jin-Liang Zhang, Ming-Liang Wang, Yue-Ming Wang, Zong-De Fang (2006) The improved F-expansion method and its applications. 350(1-2), 103-109.
Ji-Huan He, Xu-Hong Wu (2006) Exp-function method for nonlinear wave equations. 30(3), 700-708.
Hossein Aminikhah, Hossein Moosaei, Mojtaba Hajipour (2009) Exact solutions for nonlinear partial differential equations via Exp‐function method. 26(6), 1427-1433.
Z Zhang (2008) New exact traveling wave solutions for the nonlinear Klein-Gordon equation. 32, 235-240.
M Wang, J Zhang, X Li (2008) The ( )expansion method and travelling wave solutions of nonlinear evolutions equations in mathematical physics. 372, 417-423.
Sheng Zhang, Jing-Lin Tong, Wei Wang (2008) A generalized -expansion method for the mKdV equation with variable coefficients. 372(13), 2254-2257.
E Zayed, K Gepreel (2009) The ( )expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics. 50, 13502-013513.
E Zahran, M Khater (2014) Review for "Exact and Soliton Solutions of Nonlinear Evolution Equations in Mathematical Physics Using the Generalized (G′/ G)-Expansion Approach". 64(5).
Chaoqing Dai, Jiefang Zhang (2006) Jacobian elliptic function method for nonlinear differential-difference equations. 27(4), 1042-1047.
Engui Fan, Jian Zhang (2002) Applications of the Jacobi elliptic function method to special-type nonlinear equations. 305(6), 383-392.
Shikuo Liu, Zuntao Fu, Shida Liu, Qiang Zhao (2001) Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. 289(1-2), 69-74.
Published
2015-05-06
Issue
Section
License
Copyright (c) 2015 Authors and Global Journals Private Limited
This work is licensed under a Creative Commons Attribution 4.0 International License.