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Existence of solutions to the Cauchy problem and stability of kink-solutions of the nonlinear Schrödinger equation

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Literature Cited

  1. V. E. Zakharov, F. A. Kuznetsov, and A. M. Rubenchik, “Soliton stability,” Preprint No. 199, Institute of Automatics and Electrometry, Siberian Branch of the USSR Academy of Sciences, Novosibirsk (1983).

    Google Scholar 

  2. V. G. Makhan'kov, “Solitons and numerical experiments,” É. Ch. A. Ya.,14, No. 1, 123–180 (1983).

    MathSciNet  Google Scholar 

  3. I. V. Barashenkov and V. G. Makhankov, “Soliton-like excitations in a one-dimensional nuclear matter,” JINR, E2-946-73, Dubna (1984).

    Google Scholar 

  4. I. V. Barashenkov, A. D. Gocheva, V. G. Makhankov, and I. V. Puzynin, “Stability of soliton-like ‘bubbles’,” Physica,34D, No. 12, 240–254 (1989).

    MathSciNet  Google Scholar 

  5. T. B. Benjamin, “The stability of solitary waves,” Proc. R. Soc. London,328A, 153–183 (1972).

    MathSciNet  Google Scholar 

  6. P. E. Zhidkov and K. P. Kirchev, “Stability of travelling wave solutions of some equations of mathematical physics,” É. Ch. A. Ya.,16, No. 3, 597–648 (1985).

    MathSciNet  Google Scholar 

  7. P. E. Zhidkov, “Stability of the soliton solution of the nonlinear Schrödinger equation,” Differents. Uravn.,22, No. 6, 994–1004 (1986).

    MathSciNet  Google Scholar 

  8. P. E. Zhidkov, “Stability of kink-solutions for the nonlinear Schrödinger equation,” Soobshch. OIYaI, P5-87-77, Dubna (1987).

  9. D. B. Henri, J. F. Perez, W. F. Wreszinski, “Stability theory for solitary wave solutions of scalar field equations,” Commun. Math. Phys.,85, No. 3, 351–361 (1982).

    Article  Google Scholar 

  10. T. Cazenave and P. L. Lions, “Orbital stability of standing waves for some nonlinear Schrödinger equations,” Commun. Math. Phys.,85, No. 4, 549–561 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  11. M. I. Weinstein, “Lyapunov stability of ground states for nonlinear dispersive evolution equations,” Commun. Pure Appl. Math.,39, No. 1, 51–67 (1986).

    Article  MATH  Google Scholar 

  12. P. E. Zhidkov, “Solubility of the Cauchy problems and stability of certain solutions of the nonlinear Schrödinger equation,” Preprint OIYaI, P5-89-322, Dubna (1989); Matem. Model.,1, No. 10, 155–160 (1989).

  13. J. Genibre and G. Velo, “On a class of nonlinear Schrödinger equations,” J. Funct. Anal.,32, 1–32 (1979).

    Article  MathSciNet  Google Scholar 

  14. P. E. Zhidkov, “The Cauchy problem for a nonlinear Schrödinger equation,” Soobshch. OIYaI, P5-87-373, Dubna (1987).

  15. R. Bellman, Stability Theory of Solutions of Differential Equations [Russian translation], Izd. Inostr. Lit., Moscow (1954).

    Google Scholar 

  16. N. Dunford and J. Schwartz, Linear Operators. Part 2: Spectral Theory, Wiley, New York (1963).

    Google Scholar 

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Dubna. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 2, pp. 73–79, March–April, 1992.

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Zhidkov, P.E. Existence of solutions to the Cauchy problem and stability of kink-solutions of the nonlinear Schrödinger equation. Sib Math J 33, 239–246 (1992). https://doi.org/10.1007/BF00971094

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  • DOI: https://doi.org/10.1007/BF00971094

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