Riccati–Ermakov systems and explicit solutions for variable coefficient reaction–diffusion equations

Enrique Pereira, Erwin Suazo and Jessica Trespalacios

Applied Mathematics and Computation, 2018, vol. 329, issue C, 278-296

Abstract: We present several families of nonlinear reaction–diffusion equations with variable coefficients including generalizations of Fisher–KPP and Burgers type equations. Special exact solutions such as traveling wave, rational, triangular wave and N-wave type solutions are shown. By means of similarity transformations the variable coefficients are conditioned to satisfy Riccati or Ermakov systems of equations. When the Riccati system is used, conditions are established so that finite-time singularities might occur. We explore solution dynamics across multi-parameters. In the supplementary material, we provide a computer algebra verification of the solutions and exemplify nontrivial dynamics of the solutions.

Keywords: Similarity transformations; Variable coefficient Burgers equation; Variable coefficient Fisher–KPP equation; Riccati–Ermakov systems of ODEs; Exact solutions; Multiparameters (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318300705
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:329:y:2018:i:c:p:278-296

DOI: 10.1016/j.amc.2018.01.047

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().