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This article is cited in 3 scientific papers (total in 3 papers)
Multimode systems of nonlinear equations: Derivation, integrability,
and numerical solutions
M. Kuszner, S. B. Leble, B. Reichel Gdansk University of Technology, Gdansk, Polland
Abstract:
We consider the propagation of electromagnetic pulses in isotropic media taking a third-order nonlinearity into account. We develop a method for transforming Maxwell's equations based on a complete set of projection operators corresponding to wave-dispersion branches (in a waveguide or in matter) with the propagation direction taken into account. The most important result of applying the method is a system of equations describing the one-dimensional dynamics of pulses propagating in opposite directions without accounting for dispersion. We derive the corresponding self-action equations. We thus introduce dispersion in the media and show how the operators change. We obtain generalized Schäfer–Wayne short-pulse equations accounting for both propagation directions. In the three-dimensional problem, we focus on optic fibers with dispersive matter, deriving and numerically solving equations of the waveguide-mode interaction. We discuss the effects of the interaction of unidirectional pulses. For the coupled nonlinear Schrödinger equations, we discuss a concept of numerical integrability and apply the developed calculation schemes.
Keywords:
projection-operator method, multimode waveguide, coupled nonlinear Schrödinger equations, short-pulse equation.
Citation:
M. Kuszner, S. B. Leble, B. Reichel, “Multimode systems of nonlinear equations: Derivation, integrability,
and numerical solutions”, TMF, 168:1 (2011), 138–150; Theoret. and Math. Phys., 168:1 (2011), 974–984
Linking options:
https://www.mathnet.ru/eng/tmf6669https://doi.org/10.4213/tmf6669 https://www.mathnet.ru/eng/tmf/v168/i1/p138
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Abstract page: | 409 | Full-text PDF : | 219 | References: | 36 | First page: | 10 |
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