scholarly journals Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Eva Lang ◽  
Wilhelm Stannat
Keyword(s):  
Traveling Wave ◽  
Size Effects ◽  
Finite Size ◽  
Traveling Wave Solutions ◽  
Neural Field ◽  
Field Equations ◽  
Finite Size Effects ◽  
Wave Solutions ◽  
Neural Field Equations

scholarly journals Monotone traveling waves for delayed neural field equations

2016 ◽  
Vol 26 (10) ◽  
pp. 1919-1954 ◽  
Author(s):  
Jian Fang ◽  
Grégory Faye
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Level Sets ◽  
Single Layer ◽  
Traveling Wave Solutions ◽  
Neural Field ◽  
Field Equations ◽  
Minimal Speed ◽  
Wave Solutions ◽  
Neural Field Equations

We study the existence of traveling wave solutions and spreading properties for single-layer delayed neural field equations. We focus on the case where the kinetic dynamics are of monostable type and characterize the invasion speeds as a function of the asymptotic decay of the connectivity kernel. More precisely, we show that for exponentially bounded kernels the minimal speed of traveling waves exists and coincides with the spreading speed, which further can be explicitly characterized under a KPP type condition. We also investigate the case of algebraically decaying kernels where we prove the non-existence of traveling wave solutions and show the level sets of the solutions eventually locate in-between two exponential functions of time. The uniqueness of traveling waves modulo translation is also obtained.

scholarly journals Control of Nonlinear Wave Solutions to Neural Field Equations

2019 ◽  
Vol 18 (2) ◽  
pp. 1015-1036 ◽  
Author(s):  
Alexander Ziepke ◽  
Steffen Martens ◽  
Harald Engel
Keyword(s):  
Nonlinear Wave ◽  
Neural Field ◽  
Field Equations ◽  
Wave Solutions ◽  
Neural Field Equations ◽  
Nonlinear Wave Solutions

Traveling Wave Exact Solutions for Nonlinear Coupled Scalar Field Equations

2011 ◽  
Vol 284-286 ◽  
pp. 2053-2056
Author(s):  
Dong Bo Cao ◽  
Jia Ren Yan
Keyword(s):  
Scalar Field ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Trigonometric Function ◽  
Field Equations ◽  
Transform Method ◽  
Wave Solutions ◽  
Trigonometric Function Solutions ◽  
Scalar Field Equations

In the present paper, with the aid of symbolic computation, the nonlinear coupled scalar field equations relevant to materials physics are investigated by using the trigonometric function transform method. More exact traveling wave solutions are obtained for nonlinear coupled scalar field equations. The solutions obtained in this paper include four kinds of soliton solutions and four kinds of trigonometric function solutions.

Traveling wave solutions of the one-dimensional Boussinesq paradigm equation

2013 ◽  
Author(s):  
V. M. Vassilev ◽  
P. A. Djondjorov ◽  
M. Ts. Hadzhilazova ◽  
I. M. Mladenov
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
One Dimensional ◽  
Wave Solutions ◽  
The One

scholarly journals Lie Group Method for Solving the Negative-Order Kadomtsev–Petviashvili Equation (nKP)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 224
Author(s):  
Ghaylen Laouini ◽  
Amr M. Amin ◽  
Mohamed Moustafa
Keyword(s):  
Lie Group ◽  
Traveling Wave ◽  
Invariant Solution ◽  
Traveling Wave Solutions ◽  
Group Method ◽  
Lie Group Method ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Negative Order ◽  
Petviashvili Equation

A comprehensive study of the negative-order Kadomtsev–Petviashvili (nKP) partial differential equation by Lie group method has been presented. Initially the infinitesimal generators and symmetry reduction, which were obtained by applying the Lie group method on the negative-order Kadomtsev–Petviashvili equation, have been used for constructing the reduced equations. In particular, the traveling wave solutions for the negative-order KP equation have been derived from the reduced equations as an invariant solution. Finally, the extended improved (G′/G) method and the extended tanh method are described and applied in constructing new explicit expressions for the traveling wave solutions. Many new and more general exact solutions are obtained.

Sign in / Sign up

Export Citation Format

Share Document