Stimulated Raman scattering: An integrable system which blows up in finite time. (English) Zbl 0786.35124
Clarkson, Peter A. (ed.), Applications of analytic and geometric methods to nonlinear differential equations. Proceedings of the NATO Advanced Research Workshop, Exeter, United Kingdom, July 14-19, 1992. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 413, 155-161 (1993).
Summary: We present an extension of the spectral transform theory for solving initial-boundary value problems – describing the resonant interaction of radiation with matter – for arbitrary boundary values. The general method is only sketeched and it is illustrated here on a particularly representative example: the Stimulated Raman Scattering equations. We give the general solution for arbitrary boundary values. The natural boundary values (asymptotic state of the radiation) are shown to lead to a solution which blows up in finite time for any localized initial profile of the acoustic wave (initial state of the matter).
For the entire collection see [Zbl 0781.00011].
For the entire collection see [Zbl 0781.00011].
MSC:
| 35Q58 | Other completely integrable PDE (MSC2000) |
| 58J72 | Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds |
| 35B40 | Asymptotic behavior of solutions to PDEs |
