Results 21 to 30 of about 269 (44)

On the central quadric ansatz: integrable models and Painleve reductions [PDF]

, 2012
It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley (BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess solutions whose level surfaces are central quadrics in the space of independent variables (the so-called
A Zhang, B Huard, Calderbank D M J, Dryuma V, Dunajski M, E V Ferapontov, Ferapontov E V, Grundland A M, Huard B, Pavlov M V, Tod K P, Tsarev S P   +11 more
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Multi-integral representations for associated Legendre and Ferrers functions

, 2020
For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas.
Cohl, Howard S., Costas-Santos, Roberto S   +1 more
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Taylor Series for Adomian Decomposition Method

, 2011
In the paper we analyse the exact solutions to scalar PDEs obtained thanks to summable Taylor series provided by Adomian's decomposition method. We propose the modification of the method which makes the calculations of Taylor coefficients easier and more
Kutafina, Ekaterina
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A new mathematical formulation for a phase change problem with a memory flux [PDF]

, 2018
A mathematical formulation for a one-phase change problem in a form of Stefan problem with a memory flux is obtained. The hypothesis that the integral of weighted backward fluxes is proportional to the gradient of the temperature is considered. The model
Bollati, Julieta, Roscani, Sabrina Dina, Tarzia, Domingo Alberto   +2 more
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Second order reductions of the WDVV Equations related to classical Lie algebras [PDF]

, 2004
We construct second order reductions of the generalized Witten-Dijkgraaf-Verlinde-Verlinde system based on simple Lie algebras. We discuss to what extent some of the symmetries of the WDVV system are preserved by the reduction.Comment: 6 pages, 1 ...
A. Klemm, A. Marshakov, A. Mironov, B. Wit de, H.W. Braden, L. K. Hoevenaars, N. Nekrasov, N. Seiberg, R. Dijkgraaf, R. Martini, R. Martini, R. Martini   +11 more
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Solutions Classification to the Extended Reduced Ostrovsky Equation [PDF]

, 2008
An alternative to the Parkes' approach [SIGMA 4 (2008) 053, arXiv:0806.3155] is suggested for the solutions categorization to the extended reduced Ostrovsky equation (the exROE in Parkes' terminology).
Stepanyants, Yury
core   +4 more sources

Mathematical Structure of Relativistic Coulomb Integrals

, 2009
We show that the diagonal matrix elements $,$ where $O$ $={1,\beta,i\mathbf{\alpha n}\beta}$ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, may be considered as
A. F. Nikiforov, A. F. Nikiforov, H. A. Bethe, L. I. Schiff, N. M. Atakishiyev, R. Koekoek, S. Karlin, Sergei K. Suslov, V. M. Shabaev, V. M. Shabaev, V. M. Shabaev, W. N. Bailey   +11 more
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A Reciprocal Transformation for the Constant Astigmatism Equation [PDF]

, 2014
We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation $z_{yy} + (1/z)_{xx} + 2 = 0$. The transformation is related to the special case of the famous B\"acklund transformation of the sine-Gordon equation ...
Hlaváč, Adam, Marvan, Michal
core   +1 more source

Construction of an infinite-dimensional family of exact solutions of the Klein–Gordon equation by the hypercomplex method

Partial Differential Equations in Applied Mathematics
The Klein–Gordon equation is one of the fundamental equations of mathematical physics. Therefore, it is important to have exact solutions to this equation. There are many methods for constructing exact solutions to the Klein–Gordon equation.
Vitalii Shpakivskyi
doaj   +1 more source

The Degenerate Parametric Oscillator and Ince's Equation

, 2010
We construct Green's function for the quantum degenerate parametric oscillator in terms of standard solutions of Ince's equation in a framework of a general approach to harmonic oscillators.
Angelow A, Angelow A Trifonov D A, Berry M V, Cordero-Soto R Suazo E Suslov S K, Cordero-Soto R Suslov S K, Dodonov V V, Dodonov V V, Feynman R P, Hannay J H, Lanfear N Suslov S K, Li J-F, Lo C F, Louisell W H, Magnus W, Malkin I A, Meiler M Cordero-Soto R Suslov S K, Mertens C J, Nikiforov A F, Orszag M, Peřina J, Puri R R, Ricardo Cordero-Soto, Sergei K Suslov, Shen Y R, Smirnov Yu F, Suazo E Suslov S K, Suslov S K, Suslov S K, Takahasi H, Walls D F   +29 more
core   +1 more source