Asymptotic Behavior and Traveling Wave Solutions for Parabolic Functional Differential Equations

1987 ◽  
Vol 302 (2) ◽  
pp. 587 ◽  
Author(s):  
Klaus W. Schaaf
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Traveling Wave ◽  
Functional Differential Equations ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Functional Differential

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.

Asymptotic Behavior for Nonoscillatory Solutions of Second Order Nonlinear Functional Differential Equation

2012 ◽  
Vol 616-618 ◽  
pp. 2137-2141
Author(s):  
Zhi Min Luo ◽  
Bei Fei Chen
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Functional ◽  
Nonlinear Functional Differential Equation ◽  
Functional Differential

This paper studied the asymptotic behavior of a class of nonlinear functional differential equations by using the Bellman-Bihari inequality. We obtain results which extend and complement those in references. The results indicate that all non-oscillatory continuable solutions of equation are asymptotic to at+b as under some sufficient conditions, where a,b are real constants. An example is provided to illustrate the application of the results.

scholarly journals Integrability via Functional Expansion for the KMN Model

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1819
Author(s):  
Radu Constantinescu ◽  
Aurelia Florian
Keyword(s):  
Differential Equations ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Auxiliary Equation ◽  
First Order ◽  
Second Order Differential Equations ◽  
Functional Expansion ◽  
Wave Solutions ◽  
First Time

This paper considers issues such as integrability and how to get specific classes of solutions for nonlinear differential equations. The nonlinear Kundu–Mukherjee–Naskar (KMN) equation is chosen as a model, and its traveling wave solutions are investigated by using a direct solving method. It is a quite recent proposed approach called the functional expansion and it is based on the use of auxiliary equations. The main objectives are to provide arguments that the functional expansion offers more general solutions, and to point out how these solutions depend on the choice of the auxiliary equation. To see that, two different equations are considered, one first order and one second order differential equations. A large variety of KMN solutions are generated, part of them listed for the first time. Comments and remarks on the dependence of these solutions on the solving method and on form of the auxiliary equation, are included.

scholarly journals Exact Traveling Wave Solutions to the (2 + 1)-Dimensional Jaulent-Miodek Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yongyi Gu ◽  
Bingmao Deng ◽  
Jianming Lin
Keyword(s):  
Differential Equations ◽  
Computer Simulations ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Complex Method ◽  
Exact Traveling Wave Solutions ◽  
Applied Method ◽  
Wave Solutions

We derive exact traveling wave solutions to the (2 + 1)-dimensional Jaulent-Miodek equation by means of the complex method, and then we illustrate our main result by some computer simulations. It has presented that the applied method is very efficient and is practically well suited for the nonlinear differential equations that arise in mathematical physics.

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