Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-27T16:32:06.601Z Has data issue: false hasContentIssue false
  • English
  • Français

Quasi-additive solutions of nonlinear differential equations

Part of: General theory in ordinary differential equations

Published online by Cambridge University Press:  09 April 2009

A. S. Jones
A. S. Jones
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia 4067, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Some nonlinear second order ordinary differential equations have solutions which can be represented as sums of solutions of related equations. This paper classifies the equations for which this is possible and derives the corresponding forms.

MSC classification

Secondary: 34A25: Analytical theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 1 , February 1987 , pp. 92 - 116
Copyright
Copyright © Australian Mathematical Society 1987

References

Goursat, E. (1916), A course in mathematical analysis, Vol. II, Part I, Functions of a complex uariable (Ginn and Company, Boston).Google Scholar
Hancock, M. (1910), Lectures on the theory of elliptic functions (Whiley, New York).Google Scholar
Whitham, G. B. (1984), ‘Comments on periodic waves and solitons’, IMA journal of Applied Mathematics 32, 353–366.CrossRefGoogle Scholar
Zaitsev, A. A. (1983), ‘Formation of stationary non-linear waves by superposition of solitons’, Soviet phys. Dokl. 28 (9), 720–722.Google Scholar