Geodesic
$N$-soliton strings in four-dimensional space–time
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 430-439 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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{\textendash}time},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {430--439},
     year = {2007},
     volume = {152},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a1/}
}
TY  - JOUR
AU  - S. V. Talalov
TI  - $N$-soliton strings in four-dimensional space–time
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 430
EP  - 439
VL  - 152
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a1/
LA  - ru
ID  - TMF_2007_152_3_a1
ER  - 
%0 Journal Article
%A S. V. Talalov
%T $N$-soliton strings in four-dimensional space–time
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 430-439
%V 152
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a1/
%G ru
%F 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/

[1] M. R. Anderson, The Mathematical Theory of Cosmic Strings. Cosmic Strings in the Wire Approximation, Ser. High Energy Phys. Cosmol. Gravit., IOP Publ., Bristol, 2003 | MR | Zbl

[2] V. A. Rubakov, UFN, 171:9 (2001), 913 | DOI

[3] S. V. Talalov, TMF, 123:1 (2000), 38 | DOI | MR | Zbl

[4] S. V. Talalov, J. Phys. A, 22 (1989), 2275 | DOI | MR | Zbl

[5] B. M. Barbashov, V. V. Nesterenko, Model relyativistskoi struny v fizike adronov, Energoatomizdat, M., 1987 | MR

[6] S. P. Novikov, DAN SSSR, 260:1 (1981), 31 | MR | Zbl

[7] E. Witten, Commun. Math. Phys., 92 (1984), 455 | DOI | MR | Zbl

[8] A. K. Pogrebkov, S. V. Talalov, TMF, 70:3 (1987), 342 | DOI | MR

[9] A. K. Pogrebkov, TMF, 12:2 (1972), 209 | DOI

[10] G. P. Pronko, A. V. Razumov, L. D. Solovev, EChAYa, 14:3 (1983), 558 | MR

[11] L. A. Takhtadzhyan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | MR | Zbl | Zbl

[12] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov. Metod obratnoi zadachi, Nauka, M., 1980 | MR | MR | Zbl | Zbl

[13] S. V. Talalov, TMF, 71:3 (1987), 357 | DOI | MR | Zbl

[14] S. V. Klimenko, I. N. Nikitin, TMF, 114:3 (1998), 380 | DOI | MR | Zbl

[15] P. P. Kulish, A. G. Reiman, Zapiski nauch. sem. LOMI, 77 (1978), 134 | MR | Zbl