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/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