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Stabilization of Nonlinear wave packets by medium randomness :

This project aims to study the statistics of pulse propagation in noisy systems and analyze the Probability Distribution Function of width, amplitude, and other parameters. The main question is whether the probability distribution becomes steady at large values of z (Nonlinear Dynamical Localization). The team will employ novel theoretical methods such as the Functional Fokker-Planck equation, Weak Turbulence approach, and Instanton method to analyze the Universal equation representing modulation of nonlinear waves in a random medium. The project has potential applications in industrial fiber optics communication technology.

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Stabilization of Nonlinear wave packets by medium randomness :

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  1. Stabilization of Nonlinear wave packets by medium randomness: Mathematical Theory & Computer Modeling PI : Ildar Gabitov Co-PI:Misha Chertkov LANL, 7/20/00

  2. Non-equilibrium Statistical Mechanics of a wave packet To study: statistics of pulse propagation Noisy system z The key object: Probability Distribution Function of width, amplitude, etc... P P(b|0) The major question: Does P(b|z) become steady at large z ???? (NonlinearDynamicalLocalization ??) P(b|z) z Novel Theoretical Methods • Functional Fokker-Planck eq. (MSR ‘72-…) • “Weak Turbulence” approach (‘66-’76-…) • Instanton method (‘96-…)

  3. Basic Model Nonlinear Schrödinger eq. with multiplicative noise Universal equation describing modulation of nonlinear waves in random medium + Complex cases • Additive noise • Complex nonlinear interactions • Multi-channel, Multi-pulse propagations • etc * Numerical challenge Stochastic Nonlinear PDE

  4. Pieter’s questionnaire: • What will you do? • What is new and original? • What are the main challenges? The team chance for success? • What is expected impact? * scientific new phenomenon ? +development of methods * industrial fiber optics communication technology

  5. Funding Breakout Y00 Y01 Y02 I. Gabitov $90K $90K $90K M.Chertkov --- --- $60K Summer GRA $15K $15K --- PostDoc $40K $40K --- (P.Lushnikov) Mini workshop $5K $5K --- Collaborations: MST-10 (LANL),Deutche Telecom,Lucent, Croning,Weizmann Inst, Jerusalem,Novosibirsk

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