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Equations of the self-consistent field

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Literature cited

  1. A. A. Arsen'ev, “The existence of generalized solutions of the Vlasov equation,” Zh. Vychisl. Mat. Mat. Fiz.,15, 1 (1975).

    Google Scholar 

  2. N. Blombergen, Nonlinear Optics, Benjamin, New York (1965).

    Google Scholar 

  3. R. Balescu, Statistical Mechanics of Charged Particles, Wiley-Interscience, London-New York (1963).

    Google Scholar 

  4. N. N. Bogolyubov, Problems of the Dynamical Theory in Statistical Physics, Moscow-Leningrad (1946).

  5. K. P. Gurov, Foundations of Kinetic Theory [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  6. Yu. L. Daletskii, “Continuum integrals related to operator evolution equations,” Usp. Mat. Nauk,17, No. 5, 3–115 (1965).

    Google Scholar 

  7. Yu. N. Demkov, Variational Principles in Collision Theory [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

  8. Yu. L. Klimantovich, Kinetic Theory of a Nonideal Gas and Nonideal Plasma [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  9. V. P. Maslov, Complex Markov Chains and the Continuum Integral of Feynman for Nonlinear Equations [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  10. V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  11. A. M. Chebotarev, “The representation of the solution of an equation of Hartree type in the form of a T-mapping,” Dokl. Akad. Nauk SSSR,222, No. 5, 1037–1040 (1975).

    Google Scholar 

  12. A. A. Sokolov, Yu. M. Loskutov, and I. M. Ternov, Quantum Mechanics [in Russian], Uchpedgiz, Moscow (1962).

    Google Scholar 

  13. R. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965).

    Google Scholar 

  14. V. A. Fok, Works on Quantum Field Theory, 4th Ed., Leningrad (1957).

  15. E. S. Fradkin, “The method of Green functions in quantum field theory and statistics,” Tr. Fiz. Inst. Akad. Nauk,29, 1–130 (1965).

    Google Scholar 

  16. E. Hille and R. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc., Providence (1957).

    Google Scholar 

  17. S. A. Achmanov, R. V. Hochlov, and A. P. Suchorukov, “Self-Defocusing and self-modulation in nonlinear media,” Laserhandbuch, Vol. 2, North-Holland (1972), pp. 5–108.

    Google Scholar 

  18. T. Kato, “Quasilinear equations of evolution with applications to partial differential equations,” Lect. Notes Math.,448, 25–70 (1975).

    Google Scholar 

  19. E. Nelson, “Feynman integrals and the Schrödinger equation,” J. Math. Phys.,5, No. 3, 332–343 (1964).

    Google Scholar 

  20. H. F. Trotter, “On the product of semigroups of operators,” Proc. Am. Math. Soc.,10, No. 4, 545–551 (1959).

    Google Scholar 

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Translated from Itogi Nauki i Tekhniki, Sovremennye Problemy Matematiki, Vol. 11, pp. 153–234, 1978.

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Maslov, V.P. Equations of the self-consistent field. J Math Sci 11, 123–195 (1979). https://doi.org/10.1007/BF01084247

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