Paper

Explicit travelling waves and invariant algebraic curves

and

Published 27 April 2015 • © 2015 IOP Publishing Ltd & London Mathematical Society
, , Citation Armengol Gasull and Hector Giacomini 2015 Nonlinearity 28 1597 DOI 10.1088/0951-7715/28/6/1597

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Author e-mails

gasull@mat.uab.cat

Hector.Giacomini@lmpt.univ-tours.fr

Author affiliations

1 Dept. de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C. 08193 Bellaterra, Barcelona, Spain

2 Laboratoire de Mathématiques et Physique Théorique, Faculté des Sciences et Techniques, Université de Tours, C.N.R.S. UMR 7350, 37200 Tours, France

Dates

  1. Received 1 October 2013
  2. Accepted 30 March 2015
  3. Published

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0951-7715/28/6/1597

Abstract

We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher–Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.

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10.1088/0951-7715/28/6/1597