On the spectral theory of the integro-differential operator Lambda generating nonlinear evolution equations

DOI10.1007/BF00419309zbMath0524.34029MaRDI QIDQ585441

Vladimir S. Gerdjikov

Publication date: 1982

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

spectral theorynonlinear evolution equationsintegro-differential operator

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Ordinary differential operators (34L99)

Related Items (8)

Complete integrability, gauge equivalence and Lax representation of inhomogeneous nonlinear evolution equations ⋮ Multicomponent NLS-type equations on symmetric spaces and their reductions ⋮ Perturbation theory for nearly integrable multicomponent nonlinear PDEs ⋮ The generalized Zakharov-Shabat system and the soliton perturbations ⋮ Inverse scattering on the half-line for a first-order system with a general boundary condition ⋮ Completeness of the eigenfunctions for the Caudrey–Beals–Coifman system ⋮ Symmetries and Integrability ⋮ On the complete integrability of completely integrable systems

Cites Work

• A family of Hamiltonian structures, hierarchy of Hamiltonians, and reduction for first-order matrix differential operators
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Evolution equations, singular dispersion relations, and moving eigenvalues
• The resolvent and Hamiltonian systems
• The general structure of integrable evolution equations

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