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Difference schemes for nonlinear equations of Schrödinger and parabolic type

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Literature Cited

  1. S. A. Akhmanov, Yu. E. D'yakov, and A. S. Chirkin, Introduction to Statistical Radiophysics and Optics [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  2. S. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear Optics [in Russian], Vsesoyuz. Inst. Nauchn. i Tekhnich. Inform. (VINITI), Moscow (1964).

    Google Scholar 

  3. N. Blombergen, Nonlinear Optics [Russian translation], Mir, Moscow (1966).

    Google Scholar 

  4. B. Ya. Zel'dovich, N. F. Pilipetskii, and V. V. Shkunov, “Conversion of a wave front under forced scattering,” Uspkhi Fiz. Nauk,138, No. 2, 249–288 (1982).

    Google Scholar 

  5. Ya. M. Zhileikin, “Schrödinger approximation for equations of wave packets,” in: Current Problems of Mathematical Simulation [in Russian], Moscow State Univ. (1984), pp. 128–143.

  6. Ya. M. Zhileikin and O. V. Grigorashenko, “Comparison of wave and parabolic approximation for focussing beams,” in: Numerical Analysis in FORTRAN [in Russian], Moscow State Univ. (1983), pp. 51–55.

  7. Yu. N. Karamzin, “Difference methods in problems of nonlinear optics,” Preprint, Akad. Nauk Nauk SSSR, IPM, No. 74, 1982.

  8. Yu. N. Karamzin, “Numerical methods for some problems of nonlinear optics,” Preprint, Akad. Nauk SSSR, Inst. Prikl. Mat. (IPM), No. 73, 1982.

  9. V. V. Drits, “Difference schemes for the solution of nonlinear equations of Schrödinger type,” Diff. Uravn. Primen.,33, 67–76 (1983).

    Google Scholar 

  10. V. N. Abrashin, “Difference schemes for nonlinear hyperbolic equations. I,” Diff. Uravn.9, No. 11, 2029–2040 (1973).

    Google Scholar 

  11. V. N. Abrashin, “Difference schemes for nonlinear hyperbolic equations. II,” Diff. Uravn.,11, No. 2, 294–308 (1975).

    Google Scholar 

  12. A. B. Borisov, “Numerical solution of nonlinear equations of Schrödinger type,” in: Collection of Papers of the Faculty of Computational Mathematics and Cybernetics [in Russian], No. 38, Moscow State Univ. (1983), pp. 134–150.

  13. A. B. Borisov, “Convergence of difference schemes for the solution of nonlinear equations of Schrödinger type,” in: Current Problems of Mathematical Simulation [in Russian], Moscow State Univ. (1984), pp. 70–96.

  14. A. A. Afanas'ev, V. M. Volkov, V. V. Drits, and B. A. Samson, “Numerical method of calculating simultaneous two-wave interaction of net impulses in nonlinear media,” Preprint, Inst. Mat. (IM), Minsk (1987), No. 28 (298).

  15. T. R. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical nonlinear Schrödinger equation,” J. Comput. Physics,55, No. 2, 203–220 (1984).

    Google Scholar 

  16. A. A. Samarskii and V. B. Andreev, Difference Methods for Elliptic Equations [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  17. O. A. Ladyzhenskaya, Boundary Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  18. A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  19. A. A. Samarskii and A. V. Gulin, Stability of Difference Schemes [in Russian], Nauka, Moscow (1973).

    Google Scholar 

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Vilnius University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 30, No. 2, pp. 247–260, April–June, 1990.

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Ivanauskas, F.F. Difference schemes for nonlinear equations of Schrödinger and parabolic type. Lith Math J 30, 106–116 (1990). https://doi.org/10.1007/BF00970837

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