| Abstract: |
| GBDT version of Darboux transformation was introduced in [1] and actively developed later on (see, e.g., [2--6] and references therein). It is an important approach to the construction of explicit solutions of nonlinear integrable equations, there are interesting connections with the inverse spectral transform, and we will present also recent results on explicit solutions of dynamical systems constructed via GBDT.
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1. A.L.~Sakhnovich, \textit{Dressing procedure for solutions of nonlinear equations and the method of operator identities}, Inverse Problems { 10} (1994) 699--710.
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2. I. Gohberg, M.A. Kaashoek and A.L. Sakhnovich, \textit{Canonical systems with rational spectral densities: explicit formulas and applications}, Math. Nachr.} 194 (1998) 93--125.
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3. A.~Kostenko, A.~Sakhnovich and G.~Teschl, \textit{Commutation Methods for Schr\odinger Operators with Strongly Singular Potentials}, Math. Nachr. 285 (2012) 392--410.
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4. A.L. Sakhnovich, \textit{Dynamics of electrons and explicit solutions of Dirac--Weyl systems}, J. Phys. A: Math. Theor. 50 (2017) 115201.
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5. A.L. Sakhnovich, \textit{Dynamical canonical systems and their explicit solutions},
Discrete and Continuous Dynamical Systems A 37 (2017) 1679--1689.
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6. A.L.~Sakhnovich, L.A.~Sakhnovich and I.Ya.~Roitberg, Inverse Problems and Nonlinear Evolution Equations. Solutions, Darboux Matrices and Weyl--Titchmarsh Functions, De Gruyter, Berlin, 2013. |
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