Global dynamics of stationary solutions of the extended Fisher-Kolmogorov equation

Web of Science: 5 cites, Scopus: 10 cites, Google Scholar: cites

(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Messias, Marcelo

(FCT-UNESP(Brazil). Departamento de Matemática Estatística e Computacâo)
Da Silva, Paulo R.

(IBILCE-UNESP(Brazil). Departamento de Matemática)

Data:	2011
Resum:	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).
Ajuts:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Nota:	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.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Integrability ; Extended Fisher-Kolmogorov equation ; Poincaré compactification ; Global dynamics
Publicat a:	Journal of Mathematical Physics, Vol. 52 (2011) , p. 112701, ISSN 1089-7658

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