On a Pseudo-Differential Equation¶for Stokes Waves
✍ Scribed by J. F. Toland
- Publisher
- Springer
- Year
- 2002
- Tongue
- English
- Weight
- 92 KB
- Volume
- 162
- Category
- Article
- ISSN
- 0003-9527
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We give a complete classification of the evolution equations \(\partial u / \partial t=\) \(F\left(u, \hat{c} u / \partial x, \ldots . \hat{\sigma}^{\star} u / \partial x^{k}\right)\) which describe pseudo-spherical surfaces, without any a priori assumptions on the presence of a spectral parameter.
We study a class of nonlinear evolutionary equations generated by a pseudo-differential operator with the elliptic principal symbol and with nonlinearities of the form G(u x ) where cη 2 ≤ G(η) ≤ Cη 2 for large |η|. We demonstrate existence of a universal absorbing set, and a compact attractor, and