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39 papers · 1 filter
Generalized symmetries of remarkable (1+2)-dimensional Fokker-Planck equation
Dmytro R. Popovych, Serhii D. Koval, Roman O. Popovych
Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov…
Surprising symmetry properties and exact solutions of Kolmogorov backward equations with power diffusivity
Serhii D. Koval, Elsa Dos Santos Cardoso-Bihlo, Roman O. Popovych
Using the original advanced version of the direct method, we efficiently compute the equivalence groupoids and equivalence groups of two peculiar classes of Kolmogorov backward equ…
Subalgebras of Lie algebras. Example of sl(3,R) revisited
Yevhenii Yu. Chapovskyi, Serhii D. Koval, Olha Zhur
Revisiting the results by Winternitz [Symmetry in physics, CRM Proc. Lecture Notes 34, American Mathematical Society, Providence, RI, 2004, pp. 215-227], we thoroughly refine his c…
Extended symmetry analysis of (1+2)-dimensional fine Kolmogorov backward equation
Serhii D. Koval, Roman O. Popovych
Within the class of (1+2)-dimensional ultraparabolic linear equations, we distinguish a fine Kolmogorov backward equation with a quadratic diffusivity. Modulo the point equivalence…
The Adiabatic Wigner-Weisskopf Model
Alain Joye, Marco Merkli
We consider a slowly varying time dependent d-level atom interacting with a photon field. Restricted to the single excitation atom-field sector, the model is a time-dependent gener…
Proof of the equivalence of the symplectic forms derived from the canonical and the covariant phase space formalisms
Juan Margalef-Bentabol, Eduardo J. S. Villaseñor
We prove that, for any theory defined over a space-time with boundary, the symplectic form derived in the covariant phase space is equivalent to the one derived from the canonical…