|
|
|
|
References
|
|
| |
| 1. |
V. P. Maslov, M. V. Fedoryuk, Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 |
| 2. |
S. Yu. Dobrokhotov, D. S. Minenkov, M. Rulo, “Printsip Mopertyui–Yakobi dlya gamiltonianov vida $f(x,|p|)$ v nekotorykh dvumernykh statsionarnykh kvaziklassicheskikh zadachakh”, Matem. zametki, 97:1 (2015), 48–57 |
| 3. |
B. Yu. Sternin, V. E. Shatalov, “Characteristic Cauchy problem on a complex-analytic manifold”, Global Analysis Studies and Applications I, Lecture Notes in Mathematics, 1108, eds. Yu. G. Borisovich, Yu. E. Gliklikh, A. M. Vershik, Springer, Berlin, Heidelberg, 1984, 54–76 |
| 4. |
I. A. Bogaevskii, “Kaustiki vnutrennego rasseyaniya”, Tr. MIAN, 267 (2009), 7–13 |
| 5. |
R. A. Gerwin, “Initial value solution of Maxwell's equations in cold plasma”, Amer. J. Phys., 30 (1962), 711–715 ; E. Mazzucato, “Propagation of a Gaussian beam in a nonhomogeneous plasma”, Phys. Fluid B: Plasma Phys., 1:9 (1989), 1855–1859 ; Erratum, 2:1 (1990), 228 ; J. P. Freidberg, Ideal MHD, Cambridge Univ. Press, Cambridge, 2014; G. V. Pereverzev, “Paraxial WKB description of short wavelength eigenmodes in a tokamak”, Phys. Plasmas, 8:8 (2001), 3664–3672 ; Yu. A. Kravtsov, P. B. Berczynski, “Gaussian beams in inhomogeneous media: a review”, Stud. Geophys. Geod., 51:1 (2007), 1–36 ; R. A. Cairns, V. Fuchs, “Calculation of a wave field from ray tracing”, Nucl. Fusion, 50:9 (2010), 095001 ; С. Ю. Доброхотов, А. Кардинали, А. И. Клевин, Б. Тироцци, “Комплексный росток Маслова и высокочастотные гауссовы пучки в холодной плазме в торической области”, Докл. РАН. Матем. физ., 469:6 (2016), 666–671 |
| 6. |
A. A. Shkalikov, “Operator pencils arising in elasticity and hydrodynamics: the instability index formula”, Recent Developments in Operator Theory and Its Applications (Winnipeg, Canada, October 2–6, 1994), Operator Theory: Advance and Applications, 87, eds. I. Gohberg, P. Lancaster, P. N. Shivakumar, Birkhäuser, Basel, 1996, 358–385 |
| 7. |
V. P. Maslov, Kompleksnyi metod VKB v nelineinykh uravneniyakh, Nauka, M., 1977 ; В. В. Белов, С. Ю. Доброхотов, “Квазиклассические асимптотики Маслова с комплексными фазами. I. Общий подход”, ТМФ, 92:2 (1992), 215–254 ; В. В. Белов, О. С. Доброхотов, С. Ю. Доброхотов, “Изотропные торы, комплексный росток и индекс Маслова, нормальные формы и квазимоды многомерных спектральных задач”, Матем. заметки, 69:4 (2001), 483–515 ; С. Ю. Доброхотов, А. И. Шафаревич, “Квазиклассическое квантование изотропных многообразий гамильтоновых систем”, Топологические методы в теории гамильтоновых систем, Факториал, М., 1998, 41–114 |
| 8. |
V. M. Babich, V. S. Buldyrev, Asimptoticheskie metody v zadachakh difraktsii korotkikh voln, Nauka, M., 1972 ; J. V. Ralston, “On the construction of quasimodes associated with stable periodic orbits”, Commun. Math. Phys., 51:3 (1976), 219–242 |
| 9. |
V. P. Maslov, Operatornye metody, Nauka, M., 1973 |
| 10. |
V. V. Belov, S. Yu. Dobrokhotov, T. Ya. Tudorovskiy, “Operator separation of variables for adiabatic problems in quantum and wave mechanics”, J. Eng. Math., 55:1–4 (2016), 183–237 ; S. B. Leble, Nonlinear Waves in Waveguides with Stratification, Springer, Berlin, 1991 |
| 11. |
V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 ; R. Abraham, J. E. Marsden, Foundations of Mechanics, Benjamin/Cummings Publ., Reading, MA, 1978 ; A. V. Tsiganov, “The Maupertuis principle and canonical transformations of the extended phase space”, J. Nonlinear Math. Phys., 8:1 (2001), 157–182 ; S. Yu. Dobrokhotov, M. Rouleux, “The semi-classical Maupertuis–Jacobi correspondence for quasi-periodic Hamiltonian flows with applications to linear water waves theory”, Asymptotic. Anal., 74:1–2 (2011), 33–73 ; С. Ю. Доброхотов, М. Руло, “Квазиклассический аналог принципа Мопертюи–Якоби и его приложение к линейной теории волн на воде”, Матем. заметки, 87:3 (2010), 458–463 |