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
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
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Wigner Fizikai Kutatóközpont
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2021-01-15