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Abstract
We consider the propagation of electromagnetic pulses in isotropic media taking a third-order nonlinearityinto account. We develop a method for transforming Maxwell's equations based on a complete set ofprojection operators corresponding to wave-dispersion branches (in a waveguide or in matter) with thepropagation direction taken into account. The most important result of applying the method is a systemof equations describing the one-dimensional dynamics of pulses propagating in opposite directions withoutaccounting for dispersion. We derive the corresponding self-action equations. We thus introduce dispersionin the media and show how the operators change. We obtain generalized Sch¨afer-Wayne short-pulseequations accounting for both propagation directions. In the three-dimensional problem, we focus onoptic fibers with dispersive matter, deriving and numerically solving equations of the waveguide-modeinteraction. We discuss the effects of the interaction of unidirectional pulses. For the coupled nonlinearSchr¨odinger equations, we discuss a concept of numeric integrability and apply the developed calculationschemes.
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
THEORETICAL AND MATHEMATICAL PHYSICS
no. 168,
pages 974 - 984,
ISSN: 0040-5779 - Language:
- English
- Publication year:
- 2011
- Bibliographic description:
- Leble S., Reichel B., Kuszner M.: Multimode systems of nonlinear equations: derivation, integrability, and numerical solutions// THEORETICAL AND MATHEMATICAL PHYSICS. -Vol. 168, nr. N0. 1 (2011), s.974-984
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s11232-011-0079-x
- Verified by:
- Gdańsk University of Technology
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