Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities

2021 ◽  
Vol 71 (6) ◽  
pp. 1459-1470
Author(s):  
Kun Li ◽  
Yanli He
Keyword(s):  
Traveling Wave ◽  
Solution Method ◽  
Traveling Wave Solutions ◽  
Lower Solution ◽  
Cooperative System ◽  
Lattice Systems ◽  
Dimensional Lattice ◽  
Wave Solutions ◽  
Higher Dimensional ◽  
Lower Solution Method

Abstract In this paper, we are concerned with the existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities. By using the upper and lower solution method and Schauder’s fixed point theorem, we establish the existence of traveling wave solutions. To illustrate our results, the existence of traveling wave solutions for a nonlocal delayed higher-dimensional lattice cooperative system with two species are considered.

EXACT TRAVELING WAVE SOLUTIONS OF A HIGHER-DIMENSIONAL NONLINEAR EVOLUTION EQUATION

2010 ◽  
Vol 24 (10) ◽  
pp. 1011-1021 ◽  
Author(s):  
JONU LEE ◽  
RATHINASAMY SAKTHIVEL ◽  
LUWAI WAZZAN
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Periodic Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Higher Dimensional

The exact traveling wave solutions of (4 + 1)-dimensional nonlinear Fokas equation is obtained by using three distinct methods with symbolic computation. The modified tanh–coth method is implemented to obtain single soliton solutions whereas the extended Jacobi elliptic function method is applied to derive doubly periodic wave solutions for this higher-dimensional integrable equation. The Exp-function method gives generalized wave solutions with some free parameters. It is shown that soliton solutions and triangular solutions can be established as the limits of the Jacobi doubly periodic wave solutions.

scholarly journals New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah ◽  
M. Ali Akbar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solutions ◽  
Traveling Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equation ◽  
Traveling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions ◽  
Higher Dimensional

We construct new analytical solutions of the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

scholarly journals Stability of Traveling Waves to the Lotka-Volterra Competition Model

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Ahmad Alhasanat ◽  
Chunhua Ou
Keyword(s):  
Global Stability ◽  
Comparison Principle ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Functional Space ◽  
Cooperative System ◽  
Wave Solutions ◽  
Diffusive Model ◽  
The Stability

In this paper, the stability of traveling wave solutions to the Lotka-Volterra diffusive model is investigated. First, we convert the model into a cooperative system by a special transformation. The local and the global stability of the traveling wavefronts are studied in a weighted functional space. For the global stability, comparison principle together with the squeezing technique is applied to derive the main results.

scholarly journals Traveling Wave Solutions of a Delayed Cooperative System

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 269 ◽  
Author(s):  
Xue-Shi Li ◽  
Shuxia Pan
Keyword(s):  
Asymptotic Behavior ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Sufficient Condition ◽  
Cooperative System ◽  
Wave Solutions ◽  
Existence And Nonexistence ◽  
Functional Differential ◽  
The Stability ◽  
Functional Differential System

This paper deals with the dynamics of a delayed cooperative system without quasimonotonicity. Using the contracting rectangles, we obtain a sufficient condition on the stability of the unique positive steady state of the functional differential system. When the spatial domain is whole R , the existence and nonexistence of traveling wave solutions are investigated, during which the asymptotic behavior is investigated by the contracting rectangles.

Traveling wave solutions for a diffusive three-species intraguild predation model

2018 ◽  
Vol 11 (02) ◽  
pp. 1850022 ◽  
Author(s):  
Jian-Jhong Lin ◽  
Ting-Hui Yang
Keyword(s):  
Intraguild Predation ◽  
Traveling Wave ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Admissible Pair ◽  
Lower Solution ◽  
Minimal Speed ◽  
Wave Solutions ◽  
Contracting Rectangle

The aim of this work is to investigate the existence and non-existence of traveling wave solutions for a diffusive three-species intraguild predation model which means that one predator can eat its potential resource competitors. The method of upper–lower solution is implemented to show the existence of traveling wave solutions. In order to simplify the construction of an admissible pair of upper–lower solution, the scheme of strictly contracting rectangle is applied. Finally, the minimal speed [Formula: see text] of traveling wave solutions of the model is characterized. If the wave speed is greater than [Formula: see text], we show the existence of traveling wave solutions connecting trivial and positive equilibria by combining the upper and lower solutions with the contracting rectangle. On the other hand, if the wave speed is less than [Formula: see text], the non-existence of such solutions is also established. Furthermore, to illustrate our theoretical results, some numerical simulations are performed and biological meanings are interpreted.

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