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Construction of higher-dimensional nonlinear integrable systems and of their solutions

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Literature Cited

  1. V. E. Zakharov and A. B. Shabat, "A scheme for the integration of nonlinear evolution equations of mathematical physics by the inverse scattering method. I," Funkts. Anal. Prilozhen.,6, No. 3, 43–53 (1974).

    Google Scholar 

  2. V. E. Zahkarov and A. B. Shabat, "Integration of nonlinear equations of mathematical physics by the inverse scattering method. II," Funkts. Anal. Prilozhen.,13, No. 3, 13–22 (1970).

    Google Scholar 

  3. S. V. Manakov, "The inverse scattering transform for time-dependent Schrödinger equation and Kadomtsev—Petviashvili equation," Physica 3D,3, Nos. 1–2, 420–427 (1981).

    Google Scholar 

  4. S. V. Manakov, P. Santini, and L. A. Takhtajan, "Long-time behavior of the solutions of the Kadomtsev—Petviashvili equation," Phys. Lett.,74A, 451–454 (1980).

    Google Scholar 

  5. D. J. Kaup, "The inverse scattering solution for the full three-dimensional three-wave resonant interaction," Studies Appl. Math.,62, 75–83 (1980).

    Google Scholar 

  6. M. J. Ablowitz, D. Bar Yaacov, and A. S. Fokas, "On the inverse scattering transform for the Kadomtsev—Petviashvili equation," Studies Appl. Math.,69, 135–143 (1983).

    Google Scholar 

  7. M. J. Ablowitz and A. S. Fokas, "On the inverse scattering for the time-dependent Schrödinger equation and the associated Kadomtsev—Petviashvili (I) equation," Studies Appl. Math.,69, 211–228 (1983).

    Google Scholar 

  8. V. E. Zakharov, "The inverse scattering method," in: Solitons, R. K. Bullough and P. J. Caudrey (eds.), Springer-Verlag, Berlin (1980), pp. 243–286.

    Google Scholar 

  9. V. E. Zakharov, "Integrable systems in multidimensional space," in: Math. Problems in Theor. Physics, Lecture Notes in Phys., Vol. 153, Springer-Verlag, Berlin (1982), pp. 190–216.

    Google Scholar 

  10. V. E. Zakharov, "Multidimensional integrable systems," Report to the International Congress of Math., Warsaw (1983).

  11. S. V. Manakov, "Nonlocal Riemann problem and solvable multidimensional nonlinear equations," talk delivered at the NORDITA-Landau Institute Workshop, Copenhagen, September (1982).

  12. V. E. Zakharov and S. V. Manankov, "Multidimensional nonlinear integrable systems and methods for constructing their solutions," Zap. Nauchn. Sem. LOMI,133, 77–91 (1984).

    Google Scholar 

  13. V. E. Zakharov and A. V. Mikhailov, "On the integrability of classical spinor models in two-dimensional space—time," Commun. Math. Phys.,74, 4–40 (1980).

    Google Scholar 

  14. V. E. Zakharov and A. V. Mikhailov, "Variational principle for the equations integrable by the method of the inverse problem," Funkts. Anal. Prilozhen.,14, No. 1, 55–56 (1980).

    Google Scholar 

  15. S. V. Manakov, "The inverse scattering method and two-dimensional evolution equations," Usp. Mat. Nauk,31, No. 5, 245 (1976).

    Google Scholar 

  16. S. K. Zhdanov and B. L. Trubnikov, "Soliton chains in a plasma with magnetic viscosity," Pis'ma Zh. Eksp. Teor. Fiz.,39, No. 3, 110–113 (1983).

    Google Scholar 

  17. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevski, Theory of Solitons [in Russian], Nauka, Moscow (1980).

    Google Scholar 

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L. D. Landau Institute of Theoretical Physics, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 19, No. 2, pp. 11–25, April–June, 1985.

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Zakharov, V.E., Manakov, S.V. Construction of higher-dimensional nonlinear integrable systems and of their solutions. Funct Anal Its Appl 19, 89–101 (1985). https://doi.org/10.1007/BF01078388

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