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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.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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