8 January 2015 Analogies and distinctions between hydrodynamic and optical nonlinear waves
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Proceedings Volume 9447, 18th International School on Quantum Electronics: Laser Physics and Applications; 94471B (2015) https://doi.org/10.1117/12.2177001
Event: Eighteenth International School on Quantum Electronics: Laser Physics and Applications, 2014, Sozopol, Bulgaria
Abstract
We present the algorithm based on the Lax pair generalization to reveal some properties of nonautonomous KdV solitons. Starting from the general method of solution for the nonisospectral IST problem, we demonstrate how the varying-coefficient KdV equation can arise in nonuniformed and inhomogeneous media. We write down the one- and two-soliton solution of the nonautonomous varying-coefficient KdV with the time-dependent spectral parameter and consider some special cases of the isospectral solutions of the KdV equation with varying dispersion, nonlinearity, and gain. Finally, we compare these solutions with the nonautonomous solitons of the NLSE emphasizing their common features.
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A. Mena-Contla, R. Peña-Moreno, L. Morales-Lara, V. N. Serkin, T. L. Belyaeva, "Analogies and distinctions between hydrodynamic and optical nonlinear waves", Proc. SPIE 9447, 18th International School on Quantum Electronics: Laser Physics and Applications, 94471B (8 January 2015); doi: 10.1117/12.2177001; https://doi.org/10.1117/12.2177001
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