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Titlebook: Symmetries, Differential Equations and Applications; SDEA-III, İstanbul, Victor G. Kac,Peter J. Olver,Teoman Özer Conference proceedings 2

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Construction of Solvable Structures from , ordinary differential equation. Once the solvable structure is known, a complete set of first integrals can be computed by quadratures. Moreover, it is proved that the general solution can be obtained in parametric form and expressed in terms of solutions to a second-order linear equation.
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Differential Invariants for Two and Three Dimensional Linear Parabolic Equations,e associated invariants. We find first order invariants for the the higher dimensional parabolic equations due to an invertible change of the dependent and independent variables separately. Further, obtained invariants are employed to reduce these linear higher dimensional parabolic equations to their simplest forms.
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Kaleidoscope of Classical Vortex Images and Quantum Coherent States,We show that these states can be generated for an arbitrary . by the Quantum Fourier transform and can provide in general, qudit unit of quantum information. Relations of our states with quantum groups and quantum calculus are discussed.
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