Results 1 to 10 of about 294 (66)
On a Nonlocal Ostrovsky-Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability [PDF]
, 2010 Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm.
Golenia, Jolanta +3 more
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Exact Wave Functions for Generalized Harmonic Oscillators [PDF]
, 2011 We transform the time-dependent Schroedinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time-evolution of exact wave functions of generalized harmonic oscillators is determined in terms
Lanfear, Nathan +2 more
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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
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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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 +26 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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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 +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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Partial Differential Equations in Applied MathematicsThe 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
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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 +11 more
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