JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINARS - SPECIAL SEMINAR: ""Fundamental nonlinear equations in physics, and their fundamental solutions"

[statphys]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR

SPECIAL SEMINAR

Wednesday, 23 September 2009   -    16:30 hrs

Lecture Room D
SISSA Main Building

Boris A. MALOMED

(Tel Aviv University, Israel)

"Fundamental nonlinear equations in physics, and their fundamental 
solutions "

Abstract
A brief overview of universal equations, which govern the propagation of 
nonlinear waves in various physical media (both classical - such as 
optical fibers - and macroscopic quantum media, such as Bose-Einsten 
condensates, BECs), will be given. The survey will include the nonlinear 
Schroedinger (NLS)/Gross-Pitaevskii equations, the sine-Gordon (SG) 
equation, the Korteweg - de Vries (KdV) equation, the Kadomtsev - 
Petviashvili (KP) equations, and some others (the KP equations are 
two-dimensional models). All the above-mentioned equations, in their 
ideal form, share the fascinating property of the exact integrability, 
by means of a mathematical technique known as "the inverse-scattering 
transform". Not only are these equations ubiquitous and universal, but 
also their fundamental solutions - first of all, solitons, i.e., 
solitary waves - play a profoundly important role in all physical 
settings to which the model equations apply. Solitons have been 
predicted in a great variety of physical systems, and one-dimensional 
solitons were observed and/or created experimentally in nonlinear 
optics, BEC, long Josephson junctions (superconductivity), fluid flows, 
plasmas, etc. A great challenge to the experiment is to produce stable 
two- and three-dimensional solitons.