Stabilization of Nonlinear wave packets by medium randomness:

Mathematical Theory & Computer Modeling

PI : Ildar Gabitov

Co-PI: Misha Chertkov

LANL, 7/20/00

Non-equilibrium Statistical MechanicsNon-equilibrium Statistical Mechanics of of a wave packeta wave packet

To study: statistics of pulse propagationNoisy system

The key object:Probability Distribution Function ofwidth, 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

Basic Model Nonlinear SchrödingerNonlinear Schrödinger eq. with eq. with multiplicativemultiplicative noise noise

0||)()( 22 zczdi tz

Universal equation describing modulation of nonlinear waves in random medium

+ Complex cases •Additive noise

•Complex nonlinear interactions•Multi-channel, Multi-pulse propagations• etc

* Numerical challengeStochastic Nonlinear PDE

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?

* scientificnew phenomenon ? +development of methods

* industrialfiber optics communication technology

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