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| Content Provider | Springer Nature Link |
|---|---|
| Author | Kolesov, A. Yu. Rozov, N. Kh. |
| Copyright Year | 2009 |
| Abstract | A new phenomenon is detected that the attractors of a nonlinear wave equation can differ substantially from those of its finite-dimensional analogue obtained by replacing the spatial derivatives with corresponding difference operators (regardless of the discretization step). The presentation is based on a typical example, namely, on the boundary value problem for a Van-der-Pol-type telegraph equation with zero Neumann conditions at the ends of the unit interval. Under certain generic conditions, the problem is shown to admit only stable time-periodic motions, which are fairly numerous. When the problem is replaced by an approximating system of ordinary differential equations, the situation becomes fundamentally different: all the periodic motions (except for one or two) become unstable and, instead of them, stable two-dimensional invariant tori appear. |
| Starting Page | 1733 |
| Ending Page | 1747 |
| Page Count | 15 |
| File Format | |
| ISSN | 09655425 |
| Journal | Computational Mathematics and Mathematical Physics |
| Volume Number | 49 |
| Issue Number | 10 |
| e-ISSN | 15556662 |
| Language | English |
| Publisher | SP MAIK Nauka/Interperiodica |
| Publisher Date | 2009-10-20 |
| Publisher Place | Dordrecht |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | nonlinear telegraph equation discretization periodic motion invariant torus attractor Computational Mathematics and Numerical Analysis |
| Content Type | Text |
| Resource Type | Article |
| Subject | Computational Mathematics |
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