Preprint Article Version 1 This version is not peer-reviewed

Explicit and Exact Traveling Wave Solutions of Cahn Allen Equation Using MSE Method

Version 1 : Received: 4 January 2017 / Approved: 4 January 2017 / Online: 4 January 2017 (10:22:40 CET)

How to cite: Roshid, H.; Ali, M.Z.; Islam, M.R. Explicit and Exact Traveling Wave Solutions of Cahn Allen Equation Using MSE Method. Preprints 2017, 2017010018 (doi: 10.20944/preprints201701.0018.v1). Roshid, H.; Ali, M.Z.; Islam, M.R. Explicit and Exact Traveling Wave Solutions of Cahn Allen Equation Using MSE Method. Preprints 2017, 2017010018 (doi: 10.20944/preprints201701.0018.v1).

Abstract

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

Subject Areas

the modified simple equation method; Cahn–Allen equation; soliton solution; kink type solutions

Readers' Comments and Ratings (1)

Comment 1
Received: 9 October 2017
The commenter has declared there is no conflict of interests.
Comment: I believe that the name of Eq. (5) (with m=3) used in this preprint is inappropriate.
The authors should know that this equation is simply a particular case of the famous
FitzhughNagumo equation introduced in [1-2]. On the other hand, it is nothing elase but the real case of the classical
Newell=Whitehead model [3].
Travelling wave solutions of Eq. (5) (with m=3) were found for the first time in [4]
and then rediscovered in several papers in the 1990s
See more references in the extensive list in Chapter 1 of the recent monograph
"Nonlinear Reaction-Diffusion Systems
Conditional Symmetry, Exact Solutions and their
Applications in Biology"(2017)
http://www.springer.com/gp/book/9783319654652
The authors should compare their results with those obtained about 2530 years ago otherwise it is not clear what essentially they have done.

[1] Nagumo, J.S., Arimoto, S., Yoshizawa, S.:
An active pulse transmission line simulating nerve axon.
Proc. IRE v. 50, 2061–-2071 (1962)
[2] Fitzhugh, R.:
Impulse and physiological states in models of nerve membrane.
Biophys. J. v.1 , 445
466 (1961) [3] Newell,Alan C. and Whitehead,J. A. Finite bandwidth, finite amplitude convection
Journal = {Journal of Fluid Mechanics},
Year = {1969},
Pages = {279303}, Volume = {38},

[4] Kawahara, T., Tanaka, M.:
Interactions of traveling fronts: an exact solution of a nonlinear
diffusion equation.
Phys. Lett. A \textbf{97}, 311
314 (1983)
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