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Effective construction of two-gap solutions to the nonlinear Schrödinger equation

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References

  1. B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, “Integrable systems. 1,” in: Contemporary Problems of Mathematics. Fundamental Trends [in Russian], VINITI, Moscow, 1985, pp. 179–284. (Itogi Nauki i Tekhniki; 4)

    Google Scholar 

  2. M. V. Babich, A. I. Bobenko, and V. B. Matveev, “Solution of nonlinear equations integrable by the method of the inverse problem in theta-functions, and the symmetries of algebraic curves,” Izv. Akad. Nauk SSSR Ser. Mat., 49, No. 3, 511–529 (1985).

    MATH  Google Scholar 

  3. M. V. Babich, “Effectivation of formulas for finite-gap integration of the sine-Gordon equation for a curve of genus 3,” Funktsional. Anal. i Prilozhen., 19, No. 3, 53–55 (1985).

    Google Scholar 

  4. I. A. Taîmanov, “Effectivation of theta-function formulas for two-dimensional Schrödinger potential operators that are finite-gap at a certain energy level,” Dokl. Akad. Nauk SSSR, 285, No. 5, 1067–1070 (1985).

    Google Scholar 

  5. E. D. Belokolos, A. I. Bobenko, V. B. Matveev, and V. Z. Ènol'skiî, “Algebraic-geometric superposition principles for finite gap solutions of integrable nonlinear equations,” Uspekhi Mat. Nauk, 41, No. 2, 3–42 (1986).

    Google Scholar 

  6. R. K. Romanovskiî and S. G. Sadovnichuk, “A direct method for constructing two-gap solutions of nonlinear equations,” submitted to VINITI on December 6, 1995, No. 3234-B95.

  7. S. G. Sadovnichuk, “A. direct method for constructing three-gap solutions to nonlinear equations,” Sibirsk. Mat. Zh., 38, No. 5, 1140–1145 (1997).

    MATH  Google Scholar 

  8. R. Hirota, “Direct methods in soliton theory”, in: Solitons [Russian translation], Mir, Moscow, 1983, pp. 175–192.

    Google Scholar 

  9. A. R. Its, and V. P. Kotlyarov, “Explicit formulas for solutions of the nonlinear Schrödinger equation,” Dokl. Akad. Nauk USSR, No. 11, 965–968 (1976).

    Google Scholar 

  10. A. R. Its, “Inversion of hyperelliptic integrals and integration of nonlinear differential equations,” Vestnik Leningrad Univ., 7, 39–46 (1976).

    Google Scholar 

  11. D. Mumford, Tata Lectures on Theta [Russian translation], Mir, Moscow (1988).

    Google Scholar 

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Omsk. Translated from Sibirskiî Matematicheskiî Zhurnal, Vol. 40, No. 2, pp. 439–442, March–April, 1999.

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Romanovskiî, R.K., Sadovnichuk, S.G. Effective construction of two-gap solutions to the nonlinear Schrödinger equation. Sib Math J 40, 378–381 (1999). https://doi.org/10.1007/s11202-999-0017-4

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  • DOI: https://doi.org/10.1007/s11202-999-0017-4

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