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Mat. Sb., 1997, Volume 188, Number 1, Pages 109–128 (Mi msb190)  

This article is cited in 8 scientific papers (total in 8 papers)

On a class of elliptic potentials of the Dirac operator

A. O. Smirnov

St. Petersburg State Academy of Aerospace Equipment Construction

Abstract: We show that there exists a class of finite-gap potentials of the Dirac operator and finite-gap solutions of the 'decomposed' non-linear Schrödinger equation which are single-valued meromorphic functions of $x$. It is also shown that the evolution of the poles $x_j(t)$ of these elliptic solutions satisfies the dynamics of the Calogero–Moser system

DOI: https://doi.org/10.4213/sm190

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English version:
Sbornik: Mathematics, 1997, 188:1, 115–135

Bibliographic databases:

UDC: 517
MSC: Primary 35F25; Secondary 35J10, 35Q20
Received: 31.10.1995

Citation: A. O. Smirnov, “On a class of elliptic potentials of the Dirac operator”, Mat. Sb., 188:1 (1997), 109–128; Sb. Math., 188:1 (1997), 115–135

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gesztesy, F, “Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - An analytic approach”, Bulletin of the American Mathematical Society, 35:4 (1998), 271  crossref  mathscinet  zmath  isi
    2. J. C. Eilbeck, V. Z. Enolskii, N. A. Kostov, “Quasiperiodic and periodic solutions for vector nonlinear Schrödinger equations”, J Math Phys (N Y ), 41:12 (2000), 8236–8248  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    3. Christiansen, PL, “Quasi-periodic and periodic solutions for coupled nonlinear Schrodinger equations of Manakov type”, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 456:2001 (2000), 2263  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. E D Belokolos, J C Eilbeck, V Z Enolskii, M Salerno, J Phys A Math Gen, 34:5 (2001), 943–959  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. Kostov, NA, “Quasi-periodic and periodic solutions for dynamical systems related to Korteweg-de Vries equation”, European Physical Journal B, 29:2 (2002), 255  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus  scopus
    6. A. O. Smirnov, “Elliptic breather for nonlinear Shrödinger equation”, J. Math. Sci. (N. Y.), 192:1 (2013), 117–125  mathnet  crossref  mathscinet
    7. A. O. Smirnov, “Solution of a nonlinear Schrödinger equation in the form of two-phase freak waves”, Theoret. and Math. Phys., 173:1 (2012), 1403–1416  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    8. 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
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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