Elementary Darboux Transformations and Factorization
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 143-152
Cet article a éte moissonné depuis la source Math-Net.Ru
We prove a general theorem on factorization of polynomial matrices and use it to reduce polynomial Darboux matrices to linear ones. We discuss some new examples of linear Darboux matrices.
Mots-clés :
Darboux transformations
Keywords: Yang-Baxter equation, Zakharov–Shabat spectral problem.
Keywords: Yang-Baxter equation, Zakharov–Shabat spectral problem.
@article{TMF_2005_144_1_a14,
author = {F. Musso and A. B. Shabat},
title = {Elementary {Darboux} {Transformations} and {Factorization}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {143--152},
year = {2005},
volume = {144},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a14/}
}
F. Musso; A. B. Shabat. Elementary Darboux Transformations and Factorization. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 143-152. http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a14/
[1] V. E. Zakharov, A. B. Shabat, Funkts. analiz i ego prilozh., 13:3 (1979), 13–22 | MR | Zbl
[2] A. V. Domrin, Dokl. RAN, 390 (2003), 301–303 | MR | Zbl
[3] I. T. Khabibullin, A. G. Shagalov, TMF, 83:3 (1990), 323–333 | MR
[4] A. P. Veselov, A. B. Shabat, Funkts. analiz i ego prilozh., 27:2 (1993), 1–21 | MR | Zbl
[5] A. B. Shabat, TMF, 121:1 (1999), 165–176 | DOI | MR | Zbl
[6] V. E. Adler, V. G. Marikhin, A. B. Shabat, TMF, 129:2 (2001), 163–183 | DOI | MR | Zbl
[7] J. Hietarinta, J. Math. Phys., 34:5 (1993), 1725–1756 | DOI | MR | Zbl