Global dynamics of stationary solutions of the extended Fisher-Kolmogorov equation
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Messias, Marcelo (FCT-UNESP (Brazil). Departamento de Matemática e Computacâo)
Da Silva, Paulo R. (Ibilce - UNESP (Brasil). Departamento de Matemática)

Date:	2011
Abstract:	In this paper we study the fourth order differential equation d 4u /dt4 + q (d 2u /dt2 )+ u 3 - u = 0, which arises from the study of stationary solutions of the Extended Fisher-Kolmogorov equation. Denoting x = u, y = du/ dt , z = d 2u/ dt2 , v = d 3u/ dt3 this equation becomes equivalent to the polynomial system ˙x = y, y˙ = z, z˙ = v, v˙ = x - qz - x 3 with (x, y, z, v) ∈ R 4 and q ∈ R. As usual, the dot denotes derivative with respect to the time t. Since the system has a first integral we can reduce our analysis to a family of systems on R 3 . We provide the global phase portrait of these systems in the Poincar'e ball (i. e. in the compactification of R 3 with the sphere S 2 of the infinity).
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: J.L. is partially supported by ICREA Academia. M.M. is supported by CNPq-Brazil under the Project No. 305204/2009-2. P.R.S. is partially supported by CNPq and FAPESP. All the authors are supported by the Int. Coop. Proj. CAPES/MECD-TQED II and PHB-2009-0025.
Rights:	Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Integrability ; Extended Fisher-Kolmogorov equation ; Poincaré compactification ; Global dynamics
Published in:	Journal of mathematical physics, Vol. 52 (2011) , p. 112701, ISSN 1089-7658

DOI: 10.1063/1.3657425

Postprint 16 p, 384.2 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles