PhD type:
Fizikai Tudományok Doktori Iskola
Year:
2020/2021/2
Unit:
Wigner FK
Address of unit:
Konkoly Thege Miklós út 29 - 33, Budapest, 1121
Description:
Searching for analytic solutions of physically relevant non-linear partial differential equations
There are numerous fields in physics which deal with highly non-linear phenomena,
and take place in space and time decribed by non-linear partial differential equations (PDE)
such as wave phenomena, transport processes like fluid dynamics, plasma physics, high-energy
physics or grativation. There is no existing general mathematical theory of non-linear PDEs,
however there are some trial functions (Ansätze) like self-similar solutions, traveling
waves which give us physically relevant reasonable solutions helping to get a deeper
insight into the internal properties of such systems.
In the last decades we investigated numerous PDEs, most of them were problems from
viscous hydrodynamics [1], but heat conduction [2], non-linear electrodynamics [3] or
quantum mechanical problems [4] were addressed as well.
The candidate should have a solid knowledge in basic theoretical physics and
ordinary differential equations. We can offer problems in fluid dynamics -- which is under our
present interest --, but the research field of could be slightly changed and defined
together with the PhD candidate.
For background information see papers at: http://www.kfki.hu/~barnai
[1] I.F. Barna, M.A. Pocsai, S. Lökös and L. Mátyás
"Rayleigh-Benard convection in the generalized Oberbeck-Boussinesq system"
Chaos Solitons and Fractals. 103, (2017) 336
[2] I.F. Barna and R. Kersner
"Heat conduction: a telegraph-type model with self-similar behavior of solutions"
J. Phys. A: Math. Theor. 43, (2010) 375210
[3] I.F. Barna
"Self-similar shock wave solutions of the non-linear Maxwell equations"
Laser Phys. 24, (2014) 086002
[4] Understanding the Schrödinger Equation: Some [Non]Linear Perspectives
Editor: Valentino Simpao
I.F. Barna and L. Mátyás
"Self-similar And Travelling-Wave Analysis Of The Madelung Equations Obtained
From the Free Schrödinger Equation"
an accepted book Chapter
Nova Science Publishers 2020
Requirements:
Solid knowledge of basic theoretical physics and ordinary differential equations Good communication skills in English Basic knowledge of the Latex, Maple and Mathematica softwares
State:
Approved