scholarly journals Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system

2020 ◽  
Vol 25 (3) ◽  
Author(s):  
Aleksandra Gawlik ◽  
Vsevolod Vladimirov ◽  
Sergii Skurativskyi
Keyword(s):  
Numerical Simulation ◽  
Solitary Wave ◽  
Differential Equations ◽  
Direct Numerical Simulation ◽  
Nonlinear Differential Equations ◽  
Transport Phenomena ◽  
Nerve Impulse ◽  
Theoretical Studies ◽  
Solitary Wave Solutions ◽  
Wave Solutions

We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh–Nagumo system describing the nerve impulse propagation in axon. The modeling system is shown to possesses soliton-like solutions under certain restrictions on the parameters. The results of theoretical studies are backed by the direct numerical simulation.

Application of the Kudryashov function for finding solitary wave solutions of NLS type differential equations

Optik ◽  
2020 ◽  
Vol 224 ◽  
pp. 165519 ◽  
Author(s):  
Jayita Dan ◽  
Sharmistha Sain ◽  
A. Ghose-Choudhury ◽  
Sudip Garai
Keyword(s):  
Solitary Wave ◽  
Differential Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions

Complexiton and solitary wave solutions of the coupled nonlinear Maccari’s system using two integration schemes

2018 ◽  
Vol 32 (02) ◽  
pp. 1850014 ◽  
Author(s):  
Mustafa Inc ◽  
Aliyu Isa Aliyu ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu ◽  
Elif Nuray
Keyword(s):  
Numerical Simulation ◽  
Solitary Wave ◽  
Riccati Equation ◽  
Physical Meaning ◽  
Trigonometric Function ◽  
Solitary Wave Solutions ◽  
Integration Schemes ◽  
Wave Solutions ◽  
Trigonometric Function Solutions

In this paper, we consider a coupled nonlinear Maccari’s system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.

Sign in / Sign up

Export Citation Format

Share Document