Témakiírások
Searching for analytic solutions of physically relevant non-linear partial differential equations
témakiírás címe
Searching for analytic solutions of physically relevant non-linear partial differential equations
doktori iskola
témakiíró
tudományág
témakiírás leírása
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
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
felvehető hallgatók száma
1 fő
helyszín
Wigner Research Centre for Physics
jelentkezési határidő
2023-05-31