Polynomial solutions and other exact solutions of axisymmetric generalized Beltrami flows
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DOI: 10.1007/s00707-018-2137-z
Abstract: In this paper we have obtained different families of exact solutions for incompressible generalized Beltrami flows. We derive all possible polynomial solutions of incompressible axisymmetric generalized Beltrami flows in the variables r and z in… read more here.
Keywords: generalized beltrami; polynomial solutions; axisymmetric generalized; beltrami flows ... See more keywords
Homogeneous $$(\alpha ,k)$$(α,k)-Polynomial Solutions of the Fractional Riesz System in Hyperbolic Space
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DOI: 10.1007/s11785-017-0666-4
Abstract: In this paper we study the fractional analogous of the Laplace–Beltrami equation and the hyperbolic Riesz system studied previously by H. Leutwiler, in $${\mathbb {R}}^3$$R3. In both cases we replace the integer derivatives by Caputo… read more here.
Keywords: polynomial solutions; fractional riesz; riesz system; solutions fractional ... See more keywords
On linear equations with general polynomial solutions
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DOI: 10.1016/j.jde.2018.01.002
Abstract: Abstract We provide necessary and sufficient conditions for which an nth-order linear differential equation has a general polynomial solution. We also give necessary conditions that can directly be ascertained from the coefficient functions of the… read more here.
Keywords: polynomial solutions; linear equations; general polynomial; equations general ... See more keywords
Development of the perturbation theory using polynomial solutions
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DOI: 10.1063/1.5043487
Abstract: The number of quantum systems for which the stationary Schrodinger equation is exactly solvable is very limited. These systems constitute the basic elements of the quantum theory of perturbation. The exact polynomial solutions for real… read more here.
Keywords: polynomial solutions; development perturbation; perturbation theory; perturbation ... See more keywords
Polynomial solutions to linear PDEs with constant coefficients
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DOI: 10.1515/gmj-2019-2017
Abstract: Abstract In this note we are concerned with the question: When are the polynomial solutions to a system of linear constant coefficient PDEs dense in the set of all its solutions? read more here.
Keywords: constant coefficients; pdes constant; polynomial solutions; linear pdes ... See more keywords
Application of the DTM to the Elastic Curve Equation in Euler–Bernoulli Beam Theory
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DOI: 10.3390/math13162647
Abstract: This study demonstrates the effectiveness of the differential transform method (DTM) in solving complex solid mechanics problems, focusing on static analysis of beams under various loads and boundary conditions. For cantilever beams (BSM1), DTM provided… read more here.
Keywords: application dtm; concentrated moments; exact polynomial; polynomial solutions ... See more keywords