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

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