DISTINGUISHED SCHOLAR LECTURE
by Vladimir E. Zakharov, Regent's
AND WORKSHOP ON NONLINEAR SCIENCES
Medal of the ICTP
November 13, 2009
Arizona State University, Tempe, Arizona, U.S.A.
AREAS OF APPLIED MATHEMATICS AND NONLINEAR SCIENCES influenced by Vladimir Zakharov:
1. General theory of nonlinear waves,
Hamiltonian structures for conservative models of continuous media, canonical
transformations and normal forms of these models. Envelope
equations. Periodic stationary waves and their
stability. Solitons and their stability. Wave collapses. Nonlinear stage of parametric instability in continuous media.
Numerical simulation of nonlinear wave equations, including
numerical study of wave collapse.
2. Mathematical theory of solitons – the Inverse Scattering
Method (ISM). Integrable nonlinear wave equations, development of criteria for integrability. Asymptotic
behavior of integrable systems. Reductions in integrable systems
and their classification. The dressing method
as a generator of new integrable equations and
their exact solutions.
3. Applications of the
Inverse Scattering method to Differential Geometry. Classification of N-orthogonal coordinate systems.
Spaces of diagonal curvature and their classification.
Hyperbolic systems of Hydrodynamic type and their connection
to spaces of diagonal curvature. Application
of the Inverse Scattering method to General Relativity. Construction of new exact solutions of the Einstein equations.
4. Wave turbulence. Statistical description of
nonlinear wave fields. Derivation of kinetic
equations for waves and corrections to them. Kolmogorov-type solutions of kinetic equations and their stability.
Self-similar solutions of kinetic equations.
Coexistence of weak wave turbulence and coherent structures: solitons, quasisolitons,
collapses. Statistical description of integrable wave models. Solitonic turbulence. Intermittency in wave
turbulence. Application of weak turbulence methods
to the theory of nonlinear PDE’s. Numerical modeling of weak wave turbulence.
5. Waves in the ocean. Spectra of wind-driven sea waves on deep and shallow water.
Analytical and numerical study of wave breaking.
Interaction of ocean waves with currents. Formation
of freak waves. Wave induced transport of passive impurities. Numerical
methods for the solution of kinetic wave equation with application to development
of the wave-predicting models.
6. Nonlinear waves in optical fibers.
Optical solitons and optical
turbulence. Dispersion-managed solitons. 7. Theory of plasma turbulence
with application to astrophysics. Singular spectra of
plasma turbulence. Application of methods of
plasma turbulence to models of competition and evolution.
8. Vortex dynamics and formation
of singularities in hydrodynamics and magnetohydrodynamics with application to the theory
of hydrodynamic and MHD turbulence.
9. Weak-turbulent approach to the
theory of Bose-Einstain condensation.
Several equations, theories and effects bear his name... Asteroid 7153 "Vladzakharov"
orbits the Sun every 3.6 years. Dirac Medal of
the ICTP 2003. Zakharov's book of poems "The
Paradise for Clouds ". A
very insteresting interview ( in Russian). On his 70th birthday.
More details can be found at http://en.wikipedia.org/wiki/Vladimir_E._Zakharov
- Justin Holmer,
Brown University, Lecture: Various blow-up geometries
for the nonlinear Schroedinger equation | Abstract.pdf |
Friday, Nov 13*
- Pavel Lushnikov,
University of New Mexico, PDE/Analysis seminar talk: Critical collapse in Keller-Segel
Abstract.pdf | Lecture: Finite time singularities:
from individual collapses to collapse turbulence | Abstract.pdf |
1:45pm Introductory remarks PSA 118
2pm Lecture by Zakharov PSA 118
3-3:30pm refreshments PSA 116
3:30-5pm contributing lectures by Holmer and Lushnikov PSA 118
*event is sponsored by SoMSS and MCMSC
Saturday, Nov 14*
12noon pizza lunch with Zakharov PSA 206
students are especially welcome!
*sponsored by student SIAM chapter of ASU:
Roudenko (Chair), Arizona State University
Arizona State University
Arizona State University
Funding for this meeting is provided
by School of Mathematical and Statistical Sciences and Mathematical, Computational
and Modeling Sciences Center, Arizona State University and SIAM chapter
The url of this page is http://hahn.la.asu.edu/~suslov/Zakharov/index.html
Created by Analysis/PDE Group: A. Mahalov (ALEX.MAHALOV@asu.edu),
S. Roudenko (firstname.lastname@example.org) and
S. K. Suslov (email@example.com ) on Thursday, October 15, 2009.
Last update made on Tue, Nov 10, 2009