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- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Springer International Publishing AG
- Subject
- Mathematics; Mathematics, general; Dynamical Systems and Ergodic Theory; Difference and Functional Equations
- ISSN
- 1575-5460
- eISSN
- 1662-3592
- DOI
- 10.1007/s12346-017-0245-0
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Qualitative Theory of Dynamical Systems – Springer Journals
Published: Jun 27, 2017