RUS  ENG
Full version
JOURNALS // Matematicheskie Zametki

Mat. Zametki, 1988, Volume 44, Issue 3, Pages 319–340 (Mi mzm4249)

Resonances in asymptotic solutions of the Cauchy problem for the Schrödinger equation with rapidly oscillating finite-zone potential
S. Yu. Dobrokhotov

This publication is cited in the following articles:
  1. S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Metod osredneniya dlya zadach o kvaziklassicheskikh asimptotikakh”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy matematicheskogo obrazovaniya, SMFN, 70, no. 1, Rossiiskii universitet druzhby narodov, M., 2024, 53–76  mathnet  crossref
  2. S. Yu. Dobrokhotov, “Asymptotics of the Cauchy Problem for the One-Dimensional Schrödinger Equation with Rapidly Oscillating Initial Data and Small Addition to the Smooth Potential”, Russ. J. Math. Phys., 30:4 (2023), 466  crossref
  3. Andrii A. Plugin, Tatyana O. Kostiuk, Oleksiy A. Plugin, Dmytro O. Bondarenko, Yulia A. Sukhanova, Natalia N. Partala, “Interaction of Mineral and Polymer Fibers with Cement Stone and their Effect on the Physical-Mechanical Properties of Cement Composites”, JERA, 31 (2017), 59  crossref
  4. A. Ya. Maltsev, “On the canonical forms of the multi-dimensional averaged Poisson brackets”, Journal of Mathematical Physics, 57:5 (2016)  crossref
  5. A. Ya. Maltsev, “On the minimal set of conservation laws and the Hamiltonian structure of the Whitham equations”, Journal of Mathematical Physics, 56:2 (2015)  crossref
  6. A. Ya. Maltsev, “The multi-dimensional Hamiltonian structures in the Whitham method”, Journal of Mathematical Physics, 54:5 (2013)  crossref
  7. Andrei Ya. Maltsev, “Whitham's Method and Dubrovin–Novikov Bracket in Single-Phase and Multiphase Cases”, SIGMA, 8 (2012), 103, 54 pp.  mathnet  crossref
  8. A Ya Maltsev, “The conservation of the Hamiltonian structures in the deformations of the Whitham systems”, J. Phys. A: Math. Theor., 43:6 (2010), 065202  crossref
  9. Belov, VV, “Operator separation of variables for adiabatic problems in quantum and wave mechanics”, Journal of Engineering Mathematics, 55:1–4 (2006), 183  crossref  isi
  10. O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230  mathnet  crossref  mathscinet  zmath  elib
  11. V. V. Belov, S. Yu. Dobrokhotov, S. O. Sinitsyn, “Asymptotic solutions of the Schrödinger equation in thin tubes”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S13–S23  mathnet  mathscinet  zmath  elib
  12. O. M. Kiselev, “Asymptotic behaviour of the solution of the two-dimensional Dirac system with rapidly oscillating coefficients”, Sb. Math., 190:2 (1999), 233–254  mathnet  crossref  crossref  mathscinet  zmath  isi
  13. V. V. Belov, S. Yu. Dobrokhotov, “Semiclassical maslov asymptotics with complex phases. I. General approach”, Theoret. and Math. Phys., 92:2 (1992), 843–868  mathnet  crossref  mathscinet  isi
  14. B. A. Dubrovin, S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory”, Russian Math. Surveys, 44:6 (1989), 35–124  mathnet  crossref  mathscinet  zmath  adsnasa


© Steklov Math. Inst. of RAS, 2025