Diophantine tori and pragmatic calculation of quasimodes for operators with integrable principal symbol

DOI10.1134/S1061920820030024zbMath1452.37071OpenAlexW3083367977MaRDI QIDQ2198322

S. Yu. Dobrokhotov, A. Yu. Anikin

Publication date: 10 September 2020

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920820030024

zbMATH Keywords

Schrödinger operatorintegrable Hamiltonian systemtransport equationpseudodifferential operator

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Pseudodifferential operators as generalizations of partial differential operators (35S05) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Schrödinger operator, Schrödinger equation (35J10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Initial value problems for PDEs with pseudodifferential operators (35S10)

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Uses Software

• Mathematica

Cites Work

• Quantum geometry and quantum mechanics of integrable systems
• Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable
• The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory
• Explicit formulas for generalized action-angle variables in a neighborhood of an isotropic torus and their application
• Introduction to the Perturbation Theory of Hamiltonian Systems
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