Nonlinear waves in a quintic FitzHugh–Nagumo model with cross diffusion: Fronts, pulses, and wave trains

2021 ◽  
Vol 31 (3) ◽  
pp. 033141
Author(s):  
Evgeny P. Zemskov ◽  
Mikhail A. Tsyganov ◽  
Klaus Kassner ◽  
Werner Horsthemke
Keyword(s):  
Nonlinear Waves ◽  
Cross Diffusion ◽  
Wave Trains

scholarly journals Stability of nonlinear waves and patterns and related topics

2018 ◽  
Vol 376 (2117) ◽  
pp. 20180001
Author(s):  
Anna Ghazaryan ◽  
Stephane Lafortune ◽  
Vahagn Manukian
Keyword(s):  
Coherent Structures ◽  
Nonlinear Waves ◽  
Dynamic Properties ◽  
Travelling Waves ◽  
Complex Structure ◽  
Nonlinear Partial Differential Equations ◽  
Theme Issue ◽  
Hybrid Techniques ◽  
Wave Trains ◽  
The Waves

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

Solitary pulses and periodic wave trains in a bistable FitzHugh-Nagumo model with cross diffusion and cross advection

2022 ◽  
Vol 105 (1) ◽  
Author(s):  
Evgeny P. Zemskov ◽  
Mikhail A. Tsyganov ◽  
Genrich R. Ivanitsky ◽  
Werner Horsthemke
Keyword(s):  
Periodic Wave ◽  
Cross Diffusion ◽  
Wave Trains

A note on the application of Whitham's method to nonlinear waves in dispersive media

1974 ◽  
Vol 11 (1) ◽  
pp. 63-76 ◽  
Author(s):  
K. B. Dysthe
Keyword(s):  
Nonlinear Waves ◽  
Wave Train ◽  
Wave Interaction ◽  
Finite Amplitude ◽  
Slow Variation ◽  
Dispersive Media ◽  
Amplitude Wave ◽  
Wave Trains ◽  
The Stability

In this paper, a method developed by Whitham for obtaining equations governing the slow variation of finite-amplitude wave trains, is slightly modified. The relevant equations describing wave-wave interaction, and self-action are derived. The stability of a finite-amplitude wave train is treated in two different ways. The possibility of having a ‘solitary modulation’ on a finite-amplitude wave train is pointed out.

Nonlinear Waves, Solitons and Chaos

2000 ◽  
Author(s):  
Eryk Infeld ◽  
George Rowlands
Keyword(s):  
Nonlinear Waves
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