Inverse problems and nonlinear evolution equations. Solutions, Darboux matrices and Weyl-Titchmarsh functions

Inna Ya. Roitberg, Alexander L. Sakhnovich, Lev A. Sakhnovich

Publication date: 19 July 2012

Published in: De Gruyter Studies in Mathematics (Search for Journal in Brave)

explicit solutions inverse problems initial-boundary value problems Dirac systems operator identities \(S\)-nodes theory Darboux matrices evolution of Weyl functions integrable nonlinear equations transfer matrix functions Weyl-Titchmarsh functions

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Operator-theoretic methods (93B28) Weyl theory and its generalizations for ordinary differential equations (34B20) Soliton equations (35Q51) Applications of operator theory to differential and integral equations (47N20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Discrete version of topics in analysis (39A12) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial-boundary value problems for systems of nonlinear higher-order PDEs (35G61) Initial-boundary value problems for systems of linear first-order PDEs (35F46)

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