TY  JOUR
AU1  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/s1234601702450
DA  20170627
UR  https://www.deepdyve.com/lp/springerjournals/algebraictravelingwavesolutionsdarbouxpolynomialsandpolynomialHrFaLGZbZR
SP  429
EP  439
VL  17
IS  2
DP  DeepDyve