by Vladimir E. Zakharov, Regent's Professor

Applied Math University of Arizona and Russian Academy of Sciences


Dirac Medal of the ICTP

November 13, 2009

School of Mathematical and Statistical Sciences

Mathematical, Computational and Modeling Sciences Center

Arizona State University, Tempe, Arizona, U.S.A.

| Schedule of the Workshop | Abstracts of the Lectures |


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.

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.

and others; see

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


| Schedule of the Workshop | Abstracts of the Lectures |

Friday, Nov 13*
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
*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:

more details...


Svetlana Roudenko (Chair), Arizona State University
Alex Mahalov, Arizona State University
Sergei Suslov, 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 at ASU.

The url of this page is .
Created by Analysis/PDE Group: A. Mahalov (, S. Roudenko ( and S. K. Suslov ( ) on Thursday, October 15, 2009.
Last update made on Tue, Nov 10, 2009