New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation
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Date
2020
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Hindawi Limited
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GOLD
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Abstract
This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). The suggested technique is implemented to obtain the solutions of space-time Kolmogorov Petrovskii Piskunov (KPP) equation and its derived equations, namely, Fitzhugh Nagumo (FHN) equation and Newell-Whitehead (NW) equation. The considered models are significant in biology. The KPP equation describes genetic model for spread of dominant gene through population. The FHN equation is imperative in the study of intercellular trigger waves. Similarly, the NW equation is applied for chemical reactions, Faraday instability, and Rayleigh-Benard convection. The proposed technique FIM can be applied to find the exact solutions of PDEs. © 2020 Yu-Ming Chu et al.
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Keywords
First-order partial differential equation, Integro-differential equation, QC1-999, Physics, Statistical and Nonlinear Physics, Partial differential equation, Fisher's equation, Periodic Wave Solutions, Applied mathematics, Mathematical analysis, Quantum mechanics, Differential equation, Physics and Astronomy, Discrete Solitons in Nonlinear Photonic Systems, Modeling and Simulation, Physical Sciences, FOS: Mathematics, Nonlinear system, Anomalous Diffusion Modeling and Analysis, Mathematics, Rogue Waves in Nonlinear Systems, Nonlinear higher-order PDEs, Ablowitz-Kaup-Newell-Segur (AKNS) system, first integral method (FIM), supersymmetric (SUSY) equations, Solutions to PDEs in closed form
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Fields of Science
01 natural sciences, 0103 physical sciences, 0101 mathematics
Citation
Chu, Yu-Ming...et al. (2020). "New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation", Advances in Mathematical Physics, Vol. 2020.
WoS Q
Q3
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Q2
OpenCitations Citation Count
9
Source
Advances in Mathematical Physics
Volume
2020
Issue
Start Page
1
End Page
14
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Scopus : 12
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