Existence and Stability of Traveling Wave Solutions for a Population Genetic Model via Singular Perturbations

1994 ◽  
Vol 54 (1) ◽  
pp. 231-248 ◽  
Author(s):  
Jack D. Dockery ◽  
Roger Lui
Keyword(s):  
Singular Perturbations ◽  
Traveling Wave ◽  
Population Genetic ◽  
Genetic Model ◽  
Traveling Wave Solutions ◽  
Population Genetic Model ◽  
Wave Solutions ◽  
Existence And Stability

TRAVELING WAVE SOLUTIONS FOR DISCRETE-TIME MODEL OF DELAYED CELLULAR NEURAL NETWORKS

2013 ◽  
Vol 23 (06) ◽  
pp. 1350107 ◽  
Author(s):  
CHENG-HSIUNG HSU ◽  
JIAN-JHONG LIN
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Cellular Neural Networks ◽  
Time Model ◽  
Discrete Time Model ◽  
Characteristic Roots ◽  
Wave Solutions ◽  
Existence And Stability

The aim of this work is to study the existence and stability of traveling wave solutions for discrete-time model of delayed cellular neural networks distributed in the one-dimensional integer lattice ℤ1. Since the dynamics of each given cell depends on its left and right neighboring cells, it is not easy to construct the traveling wave solutions. Using the method of step along with positive characteristic roots of the equations, we successfully prove the existence of traveling wave solutions. Moreover, we show that all the traveling wave solutions are unstable. We also provide some numerical results to support our results, and point out the different structures of traveling wave solutions between the continuous-time and discrete-time models.

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.

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