Exact and approximate traveling waves of reaction-diffusion systems via a variational approach

Authors

Marianito R. Rodrigo, Instituto Tecnológico Autónomo de México
Robert M. Miura, New Jersey Institute of Technology

Document Type

Article

Publication Date

4-1-2011

Abstract

Reaction-diffusion systems arise in many different areas of the physical and biological sciences, and traveling wave solutions play special roles in some of these applications. In this paper, we develop a variational formulation of the existence problem for the traveling wave solution. Our main objective is to use this variational formulation to obtain exact and approximate traveling wave solutions with error estimates. As examples, we look at the Fisher equation, the Nagumo equation, and an equation with a fourth-degree nonlinearity. Also, we apply the method to the multi-component LotkaVolterra competition-diffusion system. © 2011 World Scientific Publishing Company.

Identifier

79959709919 (Scopus)

Publication Title

Analysis and Applications

External Full Text Location

https://doi.org/10.1142/S0219530511001807

e-ISSN

17936861

ISSN

02195305

First Page

187

Last Page

199

Issue

2

Volume

9

Fund Ref

National Science Foundation

Recommended Citation

Rodrigo, Marianito R. and Miura, Robert M., "Exact and approximate traveling waves of reaction-diffusion systems via a variational approach" (2011). Faculty Publications. 11405.
https://digitalcommons.njit.edu/fac_pubs/11405