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Symmetry properties of the approximations of multidimensional generalized van der Pol equations
Mathematical Institute of the Ukrainian Academy of Sciences.
1994 (English)In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 1, no 1, p. 41-59Article in journal (Refereed) Published
Abstract [en]

The subject of the paper are symmetries of the nonlinear hyperbolic equation, $$\frac{\partial^2u}{\partial t^2} - \sum_{n=1}^N \frac{\partial^2u}{\partial^2x_n} +m^2u - \varepsilon f(u)\left(\lambda_0 \frac{\partial u}{\partial t} + \sum_{n=1}^N\lambda_n \frac{\partial u}{\partial x_n}\right) =0. $$ The case $f(u)=1-u^2$ corresponds to the generalized van der Pol equation. The equation is expanded in powers of the parameter $\varepsilon$, which stands in front of the nonlinear term, and then symmetries of the resulting chain of approximate equations are studied by means of the Lie-group technique. Emphasis is made on a special type of the function $f(u)$ which admits conformal invariance of the equation.

Place, publisher, year, edition, pages
1994. Vol. 1, no 1, p. 41-59
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-5575DOI: 10.2991/jnmp.1994.1.1.3Local ID: 3b52af20-9bfc-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-5575DiVA, id: diva2:978449
Note
Upprättat; 1994; 20070103 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approved

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Euler, NorbertEuler, Marianna

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