# Graduate School in Nonlinear Science

### Sponsored by the Danish Research Academy

**
MIDIT OFD CATS
Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies
and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and
Technical University of Denmark Building 128 Department of Chemistry
Building 321 P.O. Box 49 University of Copenhagen
DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø
Denmark Denmark Denmark
**

**NONLINEAR WAVES AND SOLITONS IN FLUIDS, PLASMAS AND OPTICS
**

**LECTURE SERIES AT RISØ AND DTU**

by** Prof. Vladimir I. Karpman**

Racah Institute of Physics,

University of Jerusalem,

Israel,

**Tuesday September 1, at 13:00 - 15:00 h**

Optics and Fluid Dynamics Department

Bldg. 128, Meeting Room

Risø National Laboratory, Roskilde

**1 and 2. Nonlinear Shallow Water Waves**

Basic equations for potential surface waves in incompressible fluids are
discussed. A number of approximations leading to different simplified
equations, in particular to Boussinesq system, Korteweg-de Vries-type
equations etc., are considered with special emphasis on soliton solutions.

**Thursday September 17, at 13:00 - 14:00 h**

Optics and Fluid Dynamics Department

Bldg. 128, Meeting Room

Risø National Laboratory, Roskilde

**3. Soliton Radiation**

Nonlinear evolution equations with high-order derivatives describing
high-order dispersive effects are discussed.
Soliton radiation as a result of these effects is considered.

**Tuesday September 15, at 14:00 - 16:00 h**

MIDIT

IMM, Bldg. 321, Room 012, DTU

Technical University of Denmark, lyngby

**4. Soliton Dynamics in Generalized Nonlinear Schrödinger Equations**

Nonlinear Schrödinger equations with additional high-order derivative
terms, describing high-order dispersive effects are considered. Soliton
dynamics with account of these effects is described.

**5. Langmuir Solitons**

Langmuir solitons, describing electrostatic ion acoustic cavities with
trapped coherent Langmuir waves, are considered. Such solitons greatly
resembles Davydov Solitons in condensed matter and bio-physics and therefore
are of general importance.
Modifications of such solitons, in particular their radiation, caused by
high-order dispersive effects, are discussed.