Geodesic
Cosymmetries of chiral-type systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 3, pp. 531-544 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider chiral-type systems admitting a Lax representation with values in a real or complex semisimple Lie algebra such that an additional regularity condition is satisfied (one of the matrices is a regular element of the Lie algebra). We prove that for a chiral-type system with vanishing torsion and a nonvanishing curvature, the existence of at least one pointwise cosymmetry is a necessary condition for the regular Lax representation.
Keywords: chiral-type systems, integrable systems, Lax representation, cosymmetries. 
@article{TMF_2024_219_3_a7,
     author = {A. V. Balandin},
     title = {Cosymmetries of chiral-type systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {531--544},
     year = {2024},
     volume = {219},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_3_a7/}
}
TY  - JOUR
AU  - A. V. Balandin
TI  - Cosymmetries of chiral-type systems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2024
SP  - 531
EP  - 544
VL  - 219
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2024_219_3_a7/
LA  - ru
ID  - TMF_2024_219_3_a7
ER  - 
%0 Journal Article
%A A. V. Balandin
%T Cosymmetries of chiral-type systems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2024
%P 531-544
%V 219
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2024_219_3_a7/
%G ru
%F TMF_2024_219_3_a7
A. V. Balandin. Cosymmetries of chiral-type systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 3, pp. 531-544. http://geodesic.mathdoc.fr/item/TMF_2024_219_3_a7/

[1] N. Burbaki, Gruppy i algebry Li, Mir, M., 1978 | MR | MR | Zbl

[2] P. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, 1993 | MR

[3] A. V. Balandin, “Characteristics of conservation laws of chiral-type systems”, Lett. Math. Phys., 105:1 (2015), 27–43, arXiv: 1310.5218 | DOI | MR

[4] D. Deturck, H. Goldschmidt, J. Talvacchia, “Connections with prescribed curvature and Yang–Mills currents: the semi-simple case”, Ann. Sci. École Norm. Sup. (4), 24:1 (1991), 57–112 | DOI | MR

[5] B. Kostant, “Lie group representations on polynomial rings”, Amer. J. Math., 85:3 (1963), 327–404 | DOI | MR

[6] V. S. Varadarajan, “On the ring of invariant polynomials on a semisimple Lie algebra”, Amer. J. Math., 90:1 (1968), 308–317 | DOI | MR

[7] K. Pohlmeyer, “Integrable Hamiltonian systems and interactions through quadratic constraints”, Commun. Math. Phys., 46:3 (1976), 207–221 | DOI | MR

[8] F. Lund, T. Regge, “Unified approach to strings and vortices with soliton solutions”, Phys. Rev. D, 14:6 (1976), 1524–1535 | DOI | MR

[9] D. K. Demskoi, A. G. Meshkov, “Predstavlenie Laksa dlya tripleta skalyarnykh polei”, TMF, 134:3 (2003), 401–415 | DOI | DOI | MR | Zbl

[10] D. K. Demskoi, V. G. Marikhin, A. G. Meshkov, “Predstavleniya Laksa dlya tripletov dvumernykh skalyarnykh polei kiralnogo tipa”, TMF, 148:2 (2006), 189–205 | DOI | DOI | MR | Zbl

[11] E. V. Ferapontov, W. K. Schief, “Surfaces of Demoulin: differential geometry, Bäcklund transformation and integrability”, J. Geom. Phys., 30:4 (1999), 343–363 | DOI | MR

[12] V. A. Andreev, “Preobrazovaniya Beklunda tsepochek Tody”, TMF, 75:3 (1988), 340–352 | DOI | MR