$N$-soliton strings in four-dimensional space--time
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 430-439
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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.
@article{TMF_2007_152_3_a1,
author = {S. V. Talalov},
title = {$N$-soliton strings in four-dimensional space--time},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {430--439},
publisher = {mathdoc},
volume = {152},
number = {3},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a1/}
}
S. V. Talalov. $N$-soliton strings in four-dimensional space--time. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 430-439. http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a1/