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Quartic normal forms for the periodic nonlinear Schrödinger equation with dispersion management
| Content Provider | Semantic Scholar |
|---|---|
| Author | Panayotaros, Panayotis |
| Copyright Year | 2003 |
| Abstract | We investigate Birkhoff normal forms for the periodic nonlinear Schrödinger equation with dispersion management. The normalization we describe is related to averaging arguments considered in the literature, and has the advantage of producing fewer resonant couplings between high spatial frequency modes. One consequence is that the normal form equations have invariant subspaces of large but finite dimension, where we can find several classes of periodic orbits. The formal arguments apply to other related dispersive systems, and to normal forms of high order. We also present a rigorous version of the normal form calculation and show that solutions of the quartic normal form equations remain close to solutions of the full system over a time that is inversely proportional to a small nonlinearity parameter. ∗email: panos@colorado.edu |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ma.utexas.edu/mp_arc/c/03/03-221.pdf |
| Alternate Webpage(s) | http://rene.ma.utexas.edu/mp_arc/c/03/03-221.pdf |
| Alternate Webpage(s) | http://rene.ma.utexas.edu/mp_arc/html/c/03/03-221.pdf |
| Alternate Webpage(s) | http://www.math.utexas.edu/mp_arc/c/03/03-221.pdf |
| Alternate Webpage(s) | https://www.ma.utexas.edu/mp_arc/c/03/03-221.pdf |
| Alternate Webpage(s) | http://www.ma.utexas.edu/mp_arc/mp_arc/c/03/03-221.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Birkhoff interpolation Class Database normalization Dispersive partial differential equation Hearing Loss, High-Frequency Nonlinear system Ocular orbit Population Parameter Quartic function Schrödinger Solutions |
| Content Type | Text |
| Resource Type | Article |
