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6 papers · 2 filters
A geometric approach to integrability of Abel differential equations
José F. Cariñena, Javier de Lucas, Manuel F. Rañada
A geometric approach is used to study the Abel first order differential equation of the first kind. The approach is based on the recently developed theory of quasi-Lie systems whic…
Enhanced preliminary group classification of a class of generalized diffusion equations
Elsa Dos Santos Cardoso-Bihlo, Alexander Bihlo, Roman O. Popovych
The method of preliminary group classification is rigorously defined, enhanced and related to the theory of group classification of differential equations. Typical weaknesses in pa…
Quantum Kinetic Evolution of Marginal Observables
V. I. Gerasimenko
We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics o…
Towards Rigorous Derivation of Quantum Kinetic Equations
V. I. Gerasimenko, Zh. A. Tsvir
We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states whic…
Conservation laws and normal forms of evolution equations
Roman O. Popovych, Artur Sergyeyev
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conse…
Dynamics of Correlations of Bose and Fermi Particles
V. I. Gerasimenko, D. O. Polishchuk
We discuss the origin of the microscopic description of correlations in quantum many-particle systems obeying Fermi-Dirac and Bose-Einstein statistics. For correlation operators th…