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Quasiradiation solution to the compound integrable model
1Institute of Automation and Electrometry, Siberian Branch of Russian Academy of Sciences, 630090 Novosibirsk, Russia. zabolotskii@iae.nsk.su
Summary
We present a new integrable model combining optical fiber pulse propagation and two-wave mixing. The study shows ultrashort pulse behavior in this compound system is described by modified nonlinear Schrödinger equation solutions.
Area of Science:
- Nonlinear physics
- Mathematical physics
- Optical physics
Background:
- Compound integrable models combine distinct nonlinear systems.
- Understanding ultrashort pulse dynamics in optical fibers and resonant media is crucial.
Purpose of the Study:
- Introduce and analyze an integrable compound model.
- Investigate ultrashort pulse generation and propagation within this model.
Main Methods:
- Utilized the matrix Riemann-Hilbert factorization approach.
- Applied inverse scattering method for nonlinear evolution equations.
- Solved spectral problems on semi-infinite intervals.
Main Results:
- Developed a compound integrable model integrating modified nonlinear Schrödinger equation and two-wave mixing equations.
- Obtained solutions for specific boundary conditions in the resonant medium.
- Demonstrated asymptotic solutions for light pulses align with quasiradiation solutions.
Conclusions:
- The compound model provides a framework for studying complex nonlinear phenomena.
- The quasiradiation solution accurately describes asymptotic ultrashort pulse behavior in the optical fiber component.