[research interests] [CV] [publications] [applied
math student seminar] [Contact info] [Teaching]
Nir Gavish
PhD
student
School of Mathematical Sciences
Tel Aviv University
Research interests:
My
research interests lie in applied mathematics. In particular,
using a combination of tools such as mathematical modeling, asymptotic
analysis, numerical methods, rigorous analysis, and collaboration with
experimentalists in order to solve problems that arise from exciting
applications.
Here
is my detailed research
statement.
My main research topic is
the theory of singular solutions of the nonlinear Schrödinger equation (NLS) in
the context of nonlinear Optics. In nonlinear Optics, the NLS models the propagation
of intense laser beams in a medium such as air, water or glass. Such intense
laser beams undergo catastrophic self-focusing up to a point of collapse where,
mathematically, the solution becomes singular.
One of the open questions in this field for more than 40 years is what is the behavior of NLS solutions as they collapse. Since the 80s, the common perception is that
all singular solutions of the NLS collapse with a single profile known as the
Townes profile.
In
my research I show that this common perception is false, by showing that there
are also NLS solutions that do not collapse with the Townes profile, but rather
collapse with a ring profile. Our prediction was later confirmed experimentally
by the nonlinear Optics laboratory in Cornell University,
in collaboration with us. Our research
also included a comprehensive numerical study of NLS solutions as they approach
singularity for which we developed a novel numerical method for solving such
singular problems.
Recently
I have also branched out of those fields into auction theory.
Scientific
publications:
Singular
standing-ring solutions of nonlinear partial differential equations
Submitted to Physica
D, 2009
- A. Ditkowsky and N. Gavish
A grid redistribution method for singular problems
Journal of
Computational physics 228: 2354-2365, 2009
- N. Gavish, G.
Fibich, L. T. Vuong and A. L. Gaeta
Predicting the filamentation
of high-power beams and pulses without numerical integration: A nonlinear
Geometrical Optics method
Physical Review A 78: 043807, 2008
Critical power of collapsing vortices
Phys. Rev. A 77:
045803, 2008
Theory of singular vortex solutions of
the nonlinear Schrodinger equation
Physica D 237: 2696-2730, 2008
- G.
Fibich, N. Gavish, and X.P. Wang
Singular ring solutions of critical
and supercritical nonlinear Schrodinger equations
Physica D 231: 55-86, 2007
paper has been selected as one of the
winners of the 2007 SIAM Student Paper Competition
- A. Ditkowski,
G. Fibich and N. Gavish
Efficient solution
of Ax(k) = b(k) using
A-1
Journal of Scientific Computing 32: 29-44, 2007
- T. D. Grow,
A. A. Ishaaya, L. T. Vuong,
A. L. Gaeta, N. Gavish, and G. Fibich
Collapse dynamics
of super-Gaussian Beams
Optics Express 14: 5468-5475, 2006
- G.
Fibich, N. Gavish and X.P. Wang
New singular
solutions of the nonlinear Schrodinger equation
Physica D 211: 193-220, 2005
Applied Math student seminar
Together with Guy Baruch, we
organize the Applied
Math student seminar here at TAU.
Here are my CV and list of
publications
Contact info
My work email is nirgvsh@ tau.ac.il.
Tel. 972-3-6406210
Lab:
Room 025,
ground floor, Schreiber building.
Internal POB:
First
floor, Schreiber building.
Mailing address:
Nir Gavish
School of Mathematical Sciences
Tel Aviv
University
Tel Aviv 69978
Israel
Teaching
Numerical
Analysis for Engineers, Semester A, 2008