Quasiradiation solution to the compound integrable model.
We introduce compound integrable models composed of different systems of nonlinear equations describing evolution of fields and matter in different space and time intervals. As an example, we investigate the integrable compound model, which includes the modified nonlinear Schrödinger equation describing propagation of ultrashort pulses in an optical fiber and system of equations describing the two-wave mixing in a resonant medium with the two-photon induced Kerr-type nonlinearity. Using the matrix Riemann-Hilbert factorization approach for nonlinear evolution equations integrable in the sense of the the inverse scattering method, we study generation of ultrashort pulses in this model. We find a solution of a spectral problem on the semi-infinite interval and solve the compound model for simple but nontrivial boundary conditions for the resonant medium. We show that an asymptotic solution for light pulse propagating in the fiber is described by the quasiradiation solution to the modified nonlinear Schrödinger equation.
Zabolotskii
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Institute of Automation and Electrometry, Siberian Branch of Russian Academy of Sciences, 630090 Novosibirsk, Russia. zabolotskii@iae.nsk.su