Abstract:
A modification of the Whitham method for equations with turning points is suggested. The phase jump at the turning point is calculated. The asymptotics of eigen-values for equations which include both local and integral nonlinearity is found.
Citation:
M. V. Karasev, A. V. Pereskokov, “Quantization rule for self-consistent field equations with local rapidly decreasing nonlinearity”, TMF, 79:2 (1989), 198–208; Theoret. and Math. Phys., 79:2 (1989), 479–486
\Bibitem{KarPer89}
\by M.~V.~Karasev, A.~V.~Pereskokov
\paper Quantization rule for self-consistent field equations with local rapidly decreasing nonlinearity
\jour TMF
\yr 1989
\vol 79
\issue 2
\pages 198--208
\mathnet{http://mi.mathnet.ru/tmf4869}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1007795}
\transl
\jour Theoret. and Math. Phys.
\yr 1989
\vol 79
\issue 2
\pages 479--486
\crossref{https://doi.org/10.1007/BF01016528}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1989CJ46600004}
Linking options:
https://www.mathnet.ru/eng/tmf4869
https://www.mathnet.ru/eng/tmf/v79/i2/p198
This publication is cited in the following 6 articles:
Shapovalov A.V. Kulagin A.E. Trifonov A.Yu., “The Gross-Pitaevskii Equation With a Nonlocal Interaction in a Semiclassical Approximation on a Curve”, Symmetry-Basel, 12:2 (2020), 201
Aleksandr L. Lisok, Aleksandr V. Shapovalov, Andrey Yu. Trifonov, “Symmetry and Intertwining Operators for the Nonlocal Gross–Pitaevskii Equation”, SIGMA, 9 (2013), 066, 21 pp.
V. V. Belov, F. N. Litvinets, A. Yu. Trifonov, “Semiclassical spectral series of a Hartree-type operator corresponding
to a rest point of the classical Hamilton–Ehrenfest system”, Theoret. and Math. Phys., 150:1 (2007), 21–33
V. V. Belov, A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical Trajectory-Coherent Approximations of Hartree-Type Equations”, Theoret. and Math. Phys., 130:3 (2002), 391–418
O. V. Zhdaneev, G. N. Serezhnikov, A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical trajectory-coherent states of the nonlinear Schrödinger equation with unitary nonlinearity”, Russ Phys J, 42:7 (1999), 598
M. V. Karasev, A. V. Pereskokov, “On connection formulas for the second Painleve transcendent. Proof of the Miles conjecture, and a quantization rule”, Russian Acad. Sci. Izv. Math., 42:3 (1994), 501–560
Citation in format AMSBIB
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