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

Harun-Or- Roshid; M. Zulfikar Ali; Md. Rafiqul Islam

doi:10.20944/preprints201701.0018.v1

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 , 445466 (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}, 311314 (1983)

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

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