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TMF, 2007, Volume 152, Number 3, Pages 430–439 (Mi tmf6100)  

This article is cited in 6 scientific papers (total in 6 papers)

$N$-soliton strings in four-dimensional space–time

S. V. Talalov

Togliatti State University

Abstract: We investigate infinite relativistic strings in the Minkowski space $E_{1,3}$ set theoretically. We show that the set of such strings is uniquely parameterized by elements of the Poincaré group $\mathcal P$, of the group $\mathcal D$ of scaling transformations of Minkowski space, and of a certain subgroup $\mathcal W_0$ of the group of Weyl transformations of the two-metric and also by elements of the set of scattering data for a pair of first-order spectral problems that are characteristic of the theory of the nonlinear Schrödinger equation. The coefficients of the spectral problems are related to the second quadratic forms of the worldsheet. In this context, we define $N$-soliton strings. We discuss a hierarchy of surfaces that occurs in this analysis and corresponds to the known hierarchy associated with the nonlinear Schrödinger equation.

Keywords: relativistic string, locally minimal surface, hierarchy for the nonlinear Schrödinger equation

DOI: https://doi.org/10.4213/tmf6100

Full text: PDF file (474 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 152:3, 1234–1242

Bibliographic databases:

Received: 30.11.2006

Citation: S. V. Talalov, “$N$-soliton strings in four-dimensional space–time”, TMF, 152:3 (2007), 430–439; Theoret. and Math. Phys., 152:3 (2007), 1234–1242

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6100
  • http://mi.mathnet.ru/eng/tmf/v152/i3/p430

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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. S. V. Talalov, “Description of braids in terms of first-order spectral problems”, Theoret. and Math. Phys., 159:1 (2009), 469–473  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. S. V. Talalov, “An anyon model”, Theoret. and Math. Phys., 165:2 (2010), 1517–1526  mathnet  crossref  crossref  isi
    3. Talalov S.V., “The Anyon Model: An Example Inspired By String Theory”, Internat J Modern Phys A, 26:16 (2011), 2757–2772  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Talalov S.V., “Planar String as an Anyon Model: Cusps, Braids and Soliton Exitations”, 7th International Conference on Quantum Theory and Symmetries (Qts7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012121  crossref  isi  scopus
    5. S. V. Talalov, “Ob effekte perenosa massy vdol kosmicheskoi struny”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(31) (2013), 259–266  mathnet  crossref  elib
    6. S. V. Talalov, “Solutions of string, vortex, and anyon types for the hierarchy of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 176:3 (2013), 1145–1155  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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