Results 11 to 20 of about 253 (26)

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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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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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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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
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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
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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
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Two different fractional Stefan problems which are convergent to the same classical Stefan problem

, 2018
Two fractional Stefan problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0,1)$ such that in the limit case ($\alpha =1$) both problems coincide with the same classical Stefan problem. For the one and the other
Atkinson, Banks, Bourkrouche, Błasik, Cannon, Caputo, Chandrasekharaiah, Erdélyi, Gurtin, Gusev, Hetnarski, Ignaczak, Joseph, Junyi, Li, Metzler, Podstrigach, Povstenko, Pskhu, Roscani, Roscani, Stankovic, Tarzia, Voller, Voller, Wright, Yuste   +26 more
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Asymptotic parabolicity for strongly damped wave equations

, 2013
For $S$ a positive selfadjoint operator on a Hilbert space, \[ \frac{d^2u}{dt}(t) + 2 F(S)\frac{du}{dt}(t) + S^2u(t)=0 \] describes a class of wave equations with strong friction or damping if $F$ is a positive Borel function.
Fragnelli, Genni, Goldstein, Gisèle Ruiz, Goldstein, Jerome A., Romanelli, Silvia   +3 more
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The Riccati System and a Diffusion-Type Equation [PDF]

, 2011
We discuss a method of constructing solution of the initial value problem for duffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems.
Suazo, Erwin, Suslov, Sergei K., Vega-Guzman, Jose M.   +2 more
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