TY - JOUR AU - Valls, Claudia AB - 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 $$\dot{x} =y$$ x ˙ = y , $$\dot{y} =-c/d y +f(x)(f'(x)+r)$$ y ˙ = - c / d y + f ( x ) ( f ′ ( x ) + r ) where f is a polynomial with $$\deg f \ge 2$$ deg f ≥ 2 , $$c,d>0$$ c , d > 0 and r are real constants. All results are of interest by themselves. TI - Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions JF - Qualitative Theory of Dynamical Systems DO - 10.1007/s12346-017-0245-0 DA - 2017-06-27 UR - https://www.deepdyve.com/lp/springer-journals/algebraic-traveling-wave-solutions-darboux-polynomials-and-polynomial-HrFaLGZbZR SP - 429 EP - 439 VL - 17 IS - 2 DP - DeepDyve ER -