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Colloquium Home >>
UCCS MATHEMATICS
COLLOQUIUM
Thursday,
February 26, 2009
12:30 p.m.-1:30 p.m.
(refreshments at 12:15 pm)
UC Room 307
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BARBARA PRINARI
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Dipartimento di Fisica
Università del Salento (Lecce)
Title: Integrable Systems, Inverse Scattering Transform and Solitons
ABSTRACT: The modeling of physical phenomena has led to an interesting class
of nonlinear PDEs, referred to as integrable systems.
Some such PDEs have
explicit solutions (solitons) that are stable,localized solitary waves,
interacting elastically with one another.
One can often solve the initial
value problem for such a PDE by expressing the PDE as the compatibility
condition of a "Lax pair" of linear
operators, and solving the two associated
linear problems.This technique is called the inverse scattering transform
(IST) method.
The IST can be applied to many equations, including (systems
of) nonlinear PDEs in one space and one time dimension (1+1 D) and two space
and one
time dimensions (2+1 D), nonlinear partial difference equations,
etc.In this talk I will review the IST method and explain how it can
be
extended to solutions that do not decay at spatial infinity.In
particular, I will discuss the vector nonlinear Schrodinger (NLS)
equation (a
coupled system of PDEs in 1+1 D) and theKadomtsev-Petviashvili (KP) equation
(a PDE in 2+1 D) in the case of
nonvanishing boundary conditions.This
extension is crucial for incorporating soliton solutions (e.g.,"dark"
solitons for the vector NLS equation and "line" solitons for the KPequation)
within the IST framework.Additionally, I will elucidate the properties and
interactions of vector
NLS solitons.
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