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Elementary Darboux transformations and factorization. (English) Zbl 1178.37085
Theor. Math. Phys. 144, No. 1, 1004-1013 (2005); translation from Teor. Mat. Fiz. 144, No. 1, 143-152 (2005).
Summary: 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.

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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[1] V. E. Zakharov and A. B. Shabat, Funct. Anal. Appl., 13, 166–174 (1980).
[2] A. V. Domrin, Dokl. Rossiiskoi Akad. Nauk, 390, 301–303 (2003).
[3] I. T. Khabibullin and A. G. Shagalov, Theor. Math. Phys., 83, 565–573 (1990). · Zbl 0723.65104
[4] A. P. Veselov and A. B. Shabat, Funct. Anal. Appl., 27, No.2, 1–21 (1993). · Zbl 0813.35099
[5] A. B. Shabat, Theor. Math. Phys., 121, 1397–1408 (1999). · Zbl 0987.35133
[6] V. E. Adler, V. G. Marikhin, and A. B. Shabat, Theor. Math. Phys., 129, 1448–1465 (2001). · Zbl 1028.00517
[7] J. Hietarinta, J. Math. Phys., 34, 1725–1756 (1993). · Zbl 0778.15016
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