2. |
- Euler, Norbert, et al.
(författare)
-
Symmetry properties of the approximations of multidimensional generalized van der Pol equations
- 1994
-
Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 1:1, s. 41-59
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|