## EVENT DETAILS AND ABSTRACT

**Interdisciplinary Seminar in Nonlinear Science**
**Title:** Self-organisation in soliton wave turbulence

**Speaker:** Professor C. Josserand

**Speaker Info:** U. Chicago

**Brief Description:**

**Special Note**:

**Abstract:**

A fascinating feature of many turbulent fluid and plasma systems is
the emergence and persistence of large-scale organized states, or
coherent structures, in the midst of small-scale turbulent
fluctuations. A familiar example is the formation of
macroscopic quasi-steady vortices in a turbulent
large Reynolds number two dimensional fluid.
Such phenomena also occur for many classical Hamiltonian
systems, even though their dynamics is formally reversible.
In the present work, we shall focus our
attention on another class of nonlinear partial differential equations
whose solutions exhibit the tendency to form persistent coherent
structures immersed in a sea of microscopic turbulent fluctuations.
This is the class of nonlinear wave systems described by the
well-known nonlinear Schrodinger equation. We will particularly
investigate a statistical approach which describe the behavior of such a
dynamics for long time for a finite number of modes. An interesting
comparison will be made between this statistical equilibrium theory
and numerical simulations. Finally, an important analogy will be
presented
between this problem and the two dimensional turbulence.

**Date:** Friday, April 30, 1999

**Time:** 2:00pm

**Where:** Tech M416

**Contact Person:** Prof. Riecke

**Contact email:** h-riecke@nwu.edu

**Contact Phone:** 847-491-8316

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Department of Mathematics, Northwestern University.