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29 January 2019 Tappert transformation in nonlinear wave theory
V. N. Serkin, T. L. Belyaeva, G. H. Corro, A. Ramírez, L. Morales-Lara, R. Peña-Moreno
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Proceedings Volume 11047, 20th International Conference and School on Quantum Electronics: Laser Physics and Applications; 1104719 (2019) https://doi.org/10.1117/12.2516022
Event: International Conference and School on Quantum Electronics "Laser Physics and Applications": ICSQE 2018, 2018, Nessebar, Bulgaria
Abstract
We review the Tappert transformation for the nonlinear Schrödinger equation and generalize it for the higher- order nonlinear Schrödinger equation (hoNLSE) model of femtosecond nonlinear optics, in which the para- meterized gravitational-like potential e¤ectively simulates the Raman self-scattering e¤ect (the soliton Raman self-frequency shift). We present the explicit gauge transformation of this model into the "free" hoNSLSE with varying in time dispersion and nonlinearity, but without external potentials. With a certain choice of the dispersion and nonlinearity parameters, hoNLSE is turning into the completely integrable physical models, for example, the Hirota equation with gravitational-like potential, for which the same reversible gauge transformation and the change of variables are fulfilled. The transformations between the proposed integrable models allowed one to obtain directly the soliton solutions of the forced nonisospectral equations - accelerating in the gravitational- like potential nonautonomous solitons - without resolving the nonisospectral IST problem with varying in time spectral parameter.
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V. N. Serkin, T. L. Belyaeva, G. H. Corro, A. Ramírez, L. Morales-Lara, and R. Peña-Moreno "Tappert transformation in nonlinear wave theory", Proc. SPIE 11047, 20th International Conference and School on Quantum Electronics: Laser Physics and Applications, 1104719 (29 January 2019); https://doi.org/10.1117/12.2516022
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KEYWORDS
Solitons
Nonlinear optics
Raman spectroscopy
Optical solitons
Femtosecond phenomena
Wave propagation
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