Resumen de Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions

Claudia Valls

• 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.