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Research Papers

Complex Wave Solutions to Mathematical Biology Models I: Newell–Whitehead–Segel and Zeldovich Equations

[+] Author and Article Information
Alper Korkmaz

Department of Mathematics,
Çankırı Karatekin University,
Çankırı 18200, Turkey
e-mail: akorkmaz@karatekin.edu.tr

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 29, 2018; final manuscript received May 21, 2018; published online June 18, 2018. Assoc. Editor: Dumitru Baleanu.

J. Comput. Nonlinear Dynam 13(8), 081004 (Jun 18, 2018) (7 pages) Paper No: CND-18-1042; doi: 10.1115/1.4040411 History: Received January 29, 2018; Revised May 21, 2018

Complex and real valued exact solutions to some reaction-diffusion equations are suggested by using homogeneous balance and Sine-Gordon equation expansion method. The predicted solution of finite series of some hyperbolic functions is determined by using some relations between the hyperbolic functions and the trigonometric functions based on Sine-Gordon equation and traveling wave transform. The Newel–Whitehead–Segel (NWSE) and Zeldovich equations (ZE) are solved explicitly. Some complex valued solutions are depicted in real and imaginary components for some particular choice of parameters.

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References

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Figures

Grahic Jump Location
Fig. 1

Real and Imaginary parts of the particular solution u1(z,t): (a) real component and (b) imaginary component

Grahic Jump Location
Fig. 2

Real and Imaginary parts of the particular solution u25(z,t): (a) real component and (b) imaginary component

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