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Stabilization of optical pulse transmission by exploiting fiber nonlinearities
We prove theoretically, that the evolution of optical solitons can be dramatically influenced in the course of nonlinear interaction with much smaller group velocity matched pulses. Even weak pump pulses can be used to control the solitons, e.g., to compensate their degradation caused by Raman-scattering.
Simulation of pulse propagation in nonlinear optical fibers
We solve numerically a generalized nonlinear Schroedinger equation by using a pseudospectral method. Integration is performed by using an eight-order Runge-Kutta scheme. The numerical method therefore differs from the commonly used split-step method. Effects such as the impact of group velocity dispersion (GVD) up to fourth-order dispersion, self phase modulation (SPM), self-steepening and intrapulse Raman scattering can be investigated with the code. Examples for the above effects are demonstrated, as well as their interplay in the context of soliton propagation and sub-picosecond pulses.
Generalized Sasa-Satsuma equation: Densities approach to new infinite hierarchy of integrable evolution equations
We derive the new infinite Sasa-Satsuma hierarchy of evolution equations using an invariant densities approach. Being significantly simpler than the Lax-pair technique, this approach does not involve ponderous 3 x3 matrices. Moreover, it allows us to explicitly obtain operators of many orders involved in the time evolution of the Sasa-Satsuma hierarchy functionals. All these operators are parts of a generalized Sasa-Satsuma equation of infinitely high order. They enter this equation with independent arbitrary real coefficients that govern the evolution pattern of this multi-parameter dynamical system.
Persistence of rouge waves in extended nonlinear Schrödinger equations : integrable Sasa-Satsuma case
We present the lowest order rogue wave solution of the Sasa-Satsuma equation (SSE) which is one of the integrable extensions of the nonlinear Schrödinger equation (NLSE). In contrast to the Peregrine solution of the NLSE, it is significantly more involved and contains polynomials of fourth order rather than second order in the corresponding expressions. The correct limiting case of Peregrine solution appears when the extension parameter of the SSE is reduced to zero.