Four Lectures: Discretization and Integrability. Discrete Spectral Symmetries

DOI10.1007/978-3-540-88111-7_4zbMath1180.35488OpenAlexW1518415702MaRDI QIDQ3613601

S. P. Novikov

Publication date: 12 March 2009

Published in: Integrability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-88111-7_4

zbMATH Keywords

integrabilitydiscrete systemdiscrete spectral symmetry

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Invariance and symmetry properties for PDEs on manifolds (58J70) Symmetries, invariants, etc. in context of PDEs (35B06)

Cites Work

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• Difference analogs of the harmonic oscillator
• Two-dimensional Schrödinger operator: inverse scattering transform and evolutional equations
• The periodic problem for the Korteweg-de Vries equation
• Three integrable Hamiltonian systems connected with isospectral deformations
• Difference Schrödinger operators with linear and exponential discrete spectra
• Method for Solving the Korteweg-deVries Equation
• Periodic fixed points of Bäcklund transformations and the Korteweg–de Vries equation
• Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds
• On the Toda Lattice. II: Inverse-Scattering Solution
• Trivalent graphs and solitons
• Integrals of nonlinear equations of evolution and solitary waves

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