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

Carregando...
Imagem de Miniatura

Data

2011-11-01

Orientador

Coorientador

Pós-graduação

Curso de graduação

Título da Revista

ISSN da Revista

Título de Volume

Editor

American Institute of Physics (AIP)

Tipo

Artigo

Direito de acesso

Acesso restrito

Resumo

In this paper we study the fourth order differential equation d(4)u/dt(4) + q d(2)u/dt(2) + 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(2)u/dt(2), v = d(3)u/dt(3) this equation becomes equivalent to the polynomial system. (x) over dot = y, (y) over dot = z, (z) over dot = v, (v) over dot = x - qz - x(3) with (x, y, z, v) is an element of R(4) and q is an element of R. As usual, the dot denotes the 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 Poincare ball (i.e., in the compactification of R(3) with the sphere S(2) of the infinity). (C) 2011 American Institute of Physics. [doi: 10.1063/1.3657425]

Descrição

Palavras-chave

Idioma

Inglês

Como citar

Journal of Mathematical Physics. Melville: Amer Inst Physics, v. 52, n. 11, p. 12, 2011.

Itens relacionados