Results 1 to 10 of about 264 (44)

GROUP FOLIATION OF DIFFERENTIAL EQUATIONS USING MOVING FRAMES

Forum of Mathematics, Sigma, 2015
We incorporate the new theory of equivariant moving frames for Lie pseudogroups into Vessiot’s method of group foliation of differential equations. The automorphic system is replaced by a set of reconstruction equations on the pseudogroup jets.
ROBERT THOMPSON, FRANCIS VALIQUETTE
doaj   +1 more source

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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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
core   +1 more source

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

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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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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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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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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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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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
core   +1 more source