Stabilization of Nonlinear wave packets by medium randomness: Mathematical Theory & Computer...
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![Page 1: Stabilization of Nonlinear wave packets by medium randomness: Mathematical Theory & Computer Modeling PI : Ildar Gabitov Co-PI: Misha Chertkov LANL, 7/20/00.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1f5503460f94c36a81/html5/thumbnails/1.jpg)
Stabilization of Nonlinear wave packets by medium randomness:
Mathematical Theory & Computer Modeling
PI : Ildar Gabitov
Co-PI: Misha Chertkov
LANL, 7/20/00
![Page 2: Stabilization of Nonlinear wave packets by medium randomness: Mathematical Theory & Computer Modeling PI : Ildar Gabitov Co-PI: Misha Chertkov LANL, 7/20/00.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1f5503460f94c36a81/html5/thumbnails/2.jpg)
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
![Page 3: Stabilization of Nonlinear wave packets by medium randomness: Mathematical Theory & Computer Modeling PI : Ildar Gabitov Co-PI: Misha Chertkov LANL, 7/20/00.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1f5503460f94c36a81/html5/thumbnails/3.jpg)
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
![Page 4: Stabilization of Nonlinear wave packets by medium randomness: Mathematical Theory & Computer Modeling PI : Ildar Gabitov Co-PI: Misha Chertkov LANL, 7/20/00.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1f5503460f94c36a81/html5/thumbnails/4.jpg)
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
![Page 5: Stabilization of Nonlinear wave packets by medium randomness: Mathematical Theory & Computer Modeling PI : Ildar Gabitov Co-PI: Misha Chertkov LANL, 7/20/00.](https://reader036.fdocuments.us/reader036/viewer/2022083005/56649f1f5503460f94c36a81/html5/thumbnails/5.jpg)
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