Proves existence, uniqueness and regularity for the time-fractional nonlinear Schrödinger equation with Hartree perturbation.
Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation
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abstract
We discuss the Hartree equation arising in the mean-field limit of large systems of bosons and explain its importance within the class of nonlinear Schroedinger equations. Of special interest to us is the Hartree equation with focusing nonlinearity (attractive two-body interactions). Rigorous results for the Hartree equation are presented concerning: 1) its derivation from the quantum theory of large systems of bosons, 2) existence and stability of Hartree solitons, and 3) its point-particle (Newtonian) limit. Some open problems are described.
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math-ph 1years
2019 1verdicts
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The fractional in time Schr\"{o}dinger equation with a Hartree perturbation
Proves existence, uniqueness and regularity for the time-fractional nonlinear Schrödinger equation with Hartree perturbation.