Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions

• Valls, Claudia ^[1]
  1. [1] Universidade de Lisboa

     Universidade de Lisboa

     Socorro, Portugal

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 2, 2018, págs. 429-439
• Idioma: inglés
• DOI: 10.1007/s12346-017-0245-0
• Enlaces
  • Texto completo
• Resumen

  • In this paper we completely characterize the existence of algebraic traveling wave solutions for the celebrated Kolmogorov–Petrovskii–Piskunov/Zeldovich equation. To do it, we find necessary and sufficient conditions in order that a polynomial linear differential equation has a polynomial solution and we classify all the Darboux polynomials of the planar system x˙=y, y˙=-c/dy+f(x)(f′(x)+r) where f is a polynomial with degf≥2, c,d>0 and r are real constants. All results are of interest by themselves.

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