Explicit travelling waves and invariant algebraic curves

Armengol Gasull, Hector Giacomini

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11 Citations (Scopus)

Abstract

© 2015 IOP Publishing Ltd & London Mathematical Society. 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.
Original languageEnglish
Pages (from-to)1597-1606
JournalNonlinearity
Volume28
Issue number6
DOIs
Publication statusPublished - 1 Jun 2015

Keywords

  • algebraic invariant solution
  • Fischer-Kolmogorov equation
  • partial differential equation
  • polynomial differential equation
  • travelling wave

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