Gap estimates of the spectrum of Hill’s equation and action variables for KdV

DOI10.1090/S0002-9947-99-02186-8zbMath0924.58074OpenAlexW1549189037MaRDI QIDQ4219175

Boris S. Mityagin, Thomas Kappeler

Publication date: 18 November 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02186-8

zbMATH Keywords

potentialweighted Sobolev spaceSchrödinger equationFourier coefficientsperiodic eigenvalues

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Applications of dynamical systems (37N99) Ergodic theorems, spectral theory, Markov operators (37A30)

Related Items

Hill's spectral curves and the invariant measure of the periodic KdV equation, Hill's potentials in weighted Sobolev spaces and their spectral gaps, On the wellposedness of the KdV/KdV2 equations and their frequency maps, Spectral gaps of the periodic Schrödinger operator when its potential is an entire function., The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations, Spectral gap asymptotics of one-dimensional Schrödinger operators with singular periodic potentials, Gap estimates of the spectrum of the Zakharov-Shabat system, On the characterization of the smoothness of skew-adjoint potentials in periodic Dirac operators, On the periodic KdV equation in weighted Sobolev spaces, On the spectral problem associated with the time-periodic nonlinear Schrödinger equation, Instability zones of a periodic 1D Dirac operator and smoothness of its potential, Riesz basis property of Hill operators with potentials in weighted spaces, Smoothness of Schrödinger operator potential in the case of Gevrey type asymptotics of the gaps., Smoothness of solutions of a nonlinear ODE, On two-sided estimates for the nonlinear Fourier transform of KdV

Cites Work

• Unnamed Item
• Fibration of the phase space for the Korteweg-de Vries equation
• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• On the Korteweg-de Vries equation: Frequencies and initial value problem
• On the symplectic structure of the phase space for periodic KdV, Toda, and defocusing NLS
• On the Korteweg-de Vries equation: Convergent Birkhoff normal form
• Canonically Conjugate Variables for the Korteweg-de Vries Equation and the Toda Lattice with Periodic Boundary Conditions
• Hill’s surfaces and their theta functions
• Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points