Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions

Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Qualitative Theory of Dynamical Systems Springer Journals

Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions

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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
D.O.I.
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

References

  • Solitons and Inverse Scattering Transform
    Ablowitz, MJ; Segur, H
  • Symmetries and Differential Equations
    Bluman, GW; Kumei, S
  • New solitons and periodic solutions and the Kadomtsev–Petviashvili equation
    Borhanifar, A; Jafari, H; Karini, SA
  • Vahdat, New periodic and soliton wave solutions for the generalized Zakharov system and $$(2+1)$$ ( 2 + 1 ) -dimensional Nizhnik–Novikov–Veselov system
    Borhanifar, A; Kabir, MM; Maryam, L
  • Explicit travelling waves and invariant algebraic curves
    Gasull, A; Giacomini, H
  • Travelling Waves in Nonlinear Diffusion Convection Reaction
    Gilding, BH; Kersner, R
  • On polynomial Liénard systems which have invariant algebraic curves
    Hayashi, M
  • The Homotopy perturbation method for nonlinear oscillatros with discontinuities
    He, JH
  • The Direct Method in Soliton Theory
    Hirota, R
  • New solitary wave solutions for the bad Boussinesq and good Boussinesq equations
    Jafari, H; Borhanifar, A; Karini, SA
  • New applications of developed Jacobi elliptic function expansion methods
    Liu, GT; Fan, TY
  • Finite bandwidth, finite amplitude convection
    Newell, AC; Whitehead, JA
  • Algebraic traveling waves for some family of reaction–diffusion equations including the Nagumo equations
    Valls, C
  • Algebraic traveling waves for the generalized Newell–Whitehead–Segel equation
    Valls, C
  • Complete characterization of algebraic traveling wave solutions for the Boussinesq, Klein–Gordon and Benjamin–Bona–Mahony equations
    Valls, C
  • Exact solutios for a compound Kdv Burgers equation
    Wang, ML
  • An improved algebra method and its applications in nonlinear wave equtaions
    Yan, ZY
  • A theory of thermal propagation of flames
    Zeldovich, YB; Frank-Kamenetskii, DA

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