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TMF, 1988, Volume 74, Number 1, Pages 29–45 (Mi tmf4166)  

This article is cited in 14 scientific papers (total in 14 papers)

Exact integration of nonlinear Schrödinger equation

A. R. Its, A. V. Rybin, M. A. Sall'

Abstract: The degeneracy of finite-gap expressions is used to obtain a manyparameter family of smooth periodic and almost periodic solutions of the nonlinear Schrödinger equation in terms of elementary functions. A scheme for obtaining these solutions by the Darboux transformation method is considered. Propagation of a soliton on an arbitrary background is studied.

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English version:
Theoretical and Mathematical Physics, 1988, 74:1, 20–32

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Received: 04.06.1986

Citation: A. R. Its, A. V. Rybin, M. A. Sall', “Exact integration of nonlinear Schrödinger equation”, TMF, 74:1 (1988), 29–45; Theoret. and Math. Phys., 74:1 (1988), 20–32

Citation in format AMSBIB
\by A.~R.~Its, A.~V.~Rybin, M.~A.~Sall'
\paper Exact integration of nonlinear Schr\"odinger equation
\jour TMF
\yr 1988
\vol 74
\issue 1
\pages 29--45
\jour Theoret. and Math. Phys.
\yr 1988
\vol 74
\issue 1
\pages 20--32

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    This publication is cited in the following articles:
    1. G. L. Alfimov, A. R. Its, N. E. Kulagin, “Modulation instability of solutions of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 84:2 (1990), 787–793  mathnet  crossref  mathscinet  zmath  isi
    2. A. V. Yurov, A. A. Yurova, “One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid”, Theoret. and Math. Phys., 147:1 (2006), 501–508  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Doktorov, EV, “Full-time dynamics of modulational instability in spinor Bose–Einstein condensates”, Physical Review A, 76:1 (2007), 013626  crossref  isi
    4. Dubard P., Gaillard P., Klein C., Matveev V.B., “On multi-rogue wave solutions of the NLS equation and positon solutions of the KdV equation”, The European Physical Journal Special Topics, 185:1 (2010), 247–258  crossref  isi
    5. Yakhshimuratov A., “The Nonlinear Schrodinger Equation with a Self-consistent Source in the Class of Periodic Functions”, Math Phys Anal Geom, 14:2 (2011), 153–169  crossref  isi
    6. Zhao P., Fan E., Hou Yu., “Algebro-Geometric Solutions and their Reductions for the Fokas-Lenells Hierarchy”, J. Nonlinear Math. Phys., 20:3 (2013), 355–393  crossref  isi
    7. Dubard P., Matveev V.B., “Multi-Rogue Waves Solutions: From the NLS to the KP-I Equation”, Nonlinearity, 26:12 (2013), R93–R125  crossref  isi
    8. A. V. Domrin, “Real-analytic solutions of the nonlinear Schrödinger equation”, Trans. Moscow Math. Soc., 75 (2014), 173–183  mathnet  crossref  elib
    9. V. B. Matveev, F. Dyubard, A. O. Smirnov, “Kvaziratsionalnye resheniya nelineinogo uravneniya Shrëdingera”, Nelineinaya dinam., 11:2 (2015), 219–240  mathnet
    10. V. B. Matveev, A. O. Smirnov, “Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach”, Theoret. and Math. Phys., 186:2 (2016), 156–182  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. P. G. Grinevich, P. M. Santini, “Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case”, Theoret. and Math. Phys., 196:3 (2018), 1294–1306  mathnet  crossref  crossref  adsnasa  isi  elib
    12. Matveev V.B. Smirnov A.O., “Akns and Nls Hierarchies, Mrw Solutions, P-N Breathers, and Beyond”, J. Math. Phys., 59:9, SI (2018), 091419  crossref  mathscinet  zmath  isi  scopus
    13. Santini P.M., “The Periodic Cauchy Problem For Pt-Symmetric Nls, i: the First Appearance of Rogue Waves, Regular Behavior Or Blow Up At Finite Times”, J. Phys. A-Math. Theor., 51:49 (2018), 495207  crossref  mathscinet  isi  scopus
    14. P. G. Grinevich, P. M. Santini, “Konechnozonnyi podkhod v periodicheskoi zadache Koshi dlya anomalnykh voln v nelineinom uravnenii Shredingera pri nalichii neskolkikh neustoichivykh mod”, UMN, 74:2(446) (2019), 27–80  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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