Finitely and infinitely sheeted solutions in some classes of nonlinear odes

V. Marinakis, T. Bountis, S. Abenda

Research output: Contribution to journalArticle

Abstract

In this paper we examine an integrable and a non-integrable class of the first order nonlinear ordinary differential equations of the type ẋ = x - xn + εg(t), x ∈ ℂ, n ∈ ℕ. We exploit, using the analysis proposed in [1], the asymptotic formulas which give the location of the singularities in the complex plane and show that there is an essential difference regarding the formation and the density of the singularities between the cases g(t) = 1 and g(t) = t. Our analytical results are combined with a numerical study of the solutions in the complex time plane.

Original languageEnglish
Pages (from-to)63-73
Number of pages11
JournalRegular and Chaotic Dynamics
Volume3
Issue number4
Publication statusPublished - 1998
Externally publishedYes

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Nonlinear ODE
Singularity
Nonlinear Ordinary Differential Equations
Asymptotic Formula
Argand diagram
Numerical Study
First-order
Class

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

Finitely and infinitely sheeted solutions in some classes of nonlinear odes. / Marinakis, V.; Bountis, T.; Abenda, S.

In: Regular and Chaotic Dynamics, Vol. 3, No. 4, 1998, p. 63-73.

Research output: Contribution to journalArticle

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