One considers the three-dimensional Hartree equations
, ΔU=¦ψ¦2. One constructs the asymptotic (h→0) solution ψ of soliton type, localized mod 0 (h∞) in a compact domain. One finds the corresponding asymptotics of the self-consistent potential U. One obtains quantification conditions on the energy of the soliton.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk. SSSR, Vol. 84, pp. 108–113, 1979.
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Karasev, M.V., Maslov, V.P. Quasiclassical soliton solutions of the Hartree equation. J Math Sci 21, 328–332 (1983). https://doi.org/10.1007/BF01660588
- Quantification Condition
- Soliton Solution
- Compact Domain
- Hartree Equation