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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 141, Number 2, Pages 228–242
DOI: https://doi.org/10.4213/tmf122 (Mi tmf122) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Green's Function of a Hartree-Type Equation with a Quadratic Potential

A. L. Lisoka, A. Yu. Trifonova, A. V. Shapovalovb

a Tomsk Polytechnic University
b Tomsk State University
Full-text PDF (293 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf122
Abstract: Using the complex WKB–Maslov method, we consider a solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically supported functions. In this class, we obtain the evolution operator explicitly. We find parametric families of symmetry operators of the Hartree-type equation. Using the symmetry operators, we construct a family of exact solutions of this equation.
Keywords: Maslov complex germ method, Hartree-type equation, symmetry operators.
Received: 14.11.2003
English version:
Theoretical and Mathematical Physics, 2004, Volume 141, Issue 2, Pages 1528–1541
DOI: https://doi.org/10.1023/B:TAMP.0000046561.88206.f9
Bibliographic databases:
Language: Russian
Citation: A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Green's Function of a Hartree-Type Equation with a Quadratic Potential”, TMF, 141:2 (2004), 228–242; Theoret. and Math. Phys., 141:2 (2004), 1528–1541
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\crossref{https://doi.org/10.1023/B:TAMP.0000046561.88206.f9}
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  • https://www.mathnet.ru/eng/tmf122
  • https://doi.org/10.4213/tmf122
  • https://www.mathnet.ru/eng/tmf/v141/i2/p228
    • This publication is cited in the following 4 articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Quasi-energy spectral series for a nonlocal Gross-Pitaevskii equation”, Russ Phys J, 50:7 (2007), 695  crossref
    3. I. V. Khirnos, F. N. Litvinets, A. Yu. Trifonov, M. A. Shipulya, “Semiclassical spectral series of the two-component Hartree-type operator”, Russ Phys J, 50:5 (2007), 497  crossref
    4. A. V. Bezverbnyi, A. S. Gogolev, R. O. Rezaev, A. Yu. Trifonov, “Nonlinear Fokker-Planck-Kolmogorov Equation in the Semiclassical Coherent Trajectory Approximation”, Russ Phys J, 48:6 (2005), 592  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:91
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