About my research interests
My primary area of research in applied mathematics is in the theory of differential equations,
concerning particularly those which arise in problems of mathematical physics and
applied mathematics.
The principal focus of my work has been on nonlinear equations, and for the most part
these involve questions of time evolution and dynamics. Questions in this area arise
in many areas of the physical sciences, and some of the topics of my research interest
include nonlinear surface and internal waves in the ocean with an emphasis on
- Stability analysis and existence of exact solutions to the Navier-Stokes equations
with free boundaries;
- Hamiltonian dynamics;
- Symmetry analysis of differential equations;
- Numerical solution of PDEs and mathematical modeling;
- Different aspects of geophysical fluid dynamics and a variety
of stratified
flow phenomena. In particular I am interested in:
- Internal gravity waves: theoretical and numerical studies
of the generation, propagation and dissipation of internal
gravity waves
in the atmosphere and ocean;
- Large amplitude waves: numerical and analytical methods for the study of the shape
and stability of large amplitude waves;
- Flow interaction with topography: the generation of solitary–like waves
by critical (or resonant) flow over topography;
- Nonlinear wave interactions;
- Parameterization of the dissipation mechanism for internal waves.
The goal of my research is to better understand of the nonlinear wave processes and
to understand
what effects the waves have on their environment.
- I enjoy collaborating with researchers from other disciplines, and I am easy to work with.
In the past 4 years, I had successfully collaborated with professors, students and industry
collaborators from various areas, such as computational science, physics,
environmental science,
Mechanical Engineering and Geoscience.
- I keep myself open looking for potential opportunities
for collaboration and at the same time
to acquire knowledge and experience
in other disciplines.
- My second plan is to build interdisciplinary research program that could involve
undergraduate students.
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