Explicit travelling waves and invariant algebraic curves

Gasull Armengol , Giacomini Hector (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

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.

Mots clés: partial differential equation; travelling wave; Fischer Kolmogorov

Domaines: Systèmes dynamiques [math.DS]

Gasull Armengol, Giacomini Hector. Explicit travelling waves and invariant algebraic curves. Nonlinearity, 2015, 28, pp.1597-1606. ⟨10.1088/0951-7715/28/6/1597⟩. ⟨hal-01170552⟩