Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2021_33_2_a1, author = {A. Yu. Anikin and S. Yu. Dobrokhotov and V. E. Nazaikinskii and A. V. Tsvetkova}, title = {Nonstandard {Liouville} tori and caustics in asymptotics in the form of {Airy} and {Bessel} functions for two-dimensional standing coastal waves}, journal = {Algebra i analiz}, pages = {5--34}, publisher = {mathdoc}, volume = {33}, number = {2}, year = {2021}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2021_33_2_a1/} }
TY - JOUR AU - A. Yu. Anikin AU - S. Yu. Dobrokhotov AU - V. E. Nazaikinskii AU - A. V. Tsvetkova TI - Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for two-dimensional standing coastal waves JO - Algebra i analiz PY - 2021 SP - 5 EP - 34 VL - 33 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/AA_2021_33_2_a1/ LA - ru ID - AA_2021_33_2_a1 ER -
%0 Journal Article %A A. Yu. Anikin %A S. Yu. Dobrokhotov %A V. E. Nazaikinskii %A A. V. Tsvetkova %T Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for two-dimensional standing coastal waves %J Algebra i analiz %D 2021 %P 5-34 %V 33 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/AA_2021_33_2_a1/ %G ru %F AA_2021_33_2_a1
A. Yu. Anikin; S. Yu. Dobrokhotov; V. E. Nazaikinskii; A. V. Tsvetkova. Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for two-dimensional standing coastal waves. Algebra i analiz, Tome 33 (2021) no. 2, pp. 5-34. http://geodesic.mathdoc.fr/item/AA_2021_33_2_a1/
[1] Babich V. M., Buldyrev V. S., Asimptoticheskie metody v zadachakh difraktsii korotkikh voln. Metod etalonnykh zadach, Nauka, M., 1972
[2] Babich V. M., Buldyrev V. S., Molotkov I. A., Prostranstvenno-vremennoi luchevoi metod: Lineinye i nelineinye volny, Izd-vo LGU, L., 1985 | MR
[3] Babich V. M., Kiselev A. P., Uprugie volny. Vysokochastotnaya teoriya, BKhV-Peterburg, Spb., 2014
[4] Babich V. M., Buldyrev V. S., “Iskusstvo asimptotiki”, Vestn. Leningr. un-ta. Ser. mat., mekh. i astronom., 1977, no. 3, 5–12 | Zbl
[5] Birman M. Sh., Solomyak M. Z., Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, LGU, L., 1980
[6] Oleinik O. A., Radkevich E. V., “Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Itogi nauki i tekhn. Mat. anal. 1969, VINITI, M., 1971, 7–252
[7] Ursell F., “Edge waves on a sloping beach”, Proc. R. Soc. Lond. A, 214 (1952), 79–97 | DOI | MR | Zbl
[8] Zhevandrov P. N., “Edge waves on a gently sloping beach: uniform asymptotics”, J. Fluid Mech., 233 (1991), 483–493 | DOI | MR | Zbl
[9] Merzon A., Zhevandrov P., “High-frequency asymptotics of edge waves on a beach of nonconstant slope”, SIAM J. Appl. Math., 59:2 (1998), 529–546 | DOI | MR
[10] Maslov V. P., Fedoryuk M. V., Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 | MR
[11] Lazutkin V. F., “Kvaziklassicheskaya asimptotika sobstvennykh funktsii. Differentsialnye uravneniya s chastnymi proizvodnymi”, Itogi nauki i tekhn. Sovrem. probl. mat. Fundam. napravleniya, 34, VINITI, M., 1988, 135–174 | MR
[12] Matveev V. S., “Asimptoticheskie sobstvennye funktsii operatora $\nabla D(x,y) \nabla,$ otvechayuschie liuvillevym metrikam, i volny na vode, zakhvachennye donnymi neodnorodnostyami”, Mat. zametki, 64:3 (1998), 414–422 | MR | Zbl
[13] Taimanov I. A., “O pervykh integralakh geodezicheskikh potokov na dvumernom tore”, Tr. Mat. in-ta RAN, 295, 2016, 241–260 | Zbl
[14] Nazaikinskii V. E., “Geometriya fazovogo prostranstva dlya volnovogo uravneniya, vyrozhdayuschegosya na granitse oblasti”, Mat. zametki, 92:1 (2012), 153–156 | Zbl
[15] Dobrokhotov S. Yu., Nazaikinskii V. E., “Uniformizatsiya uravnenii s granichnym vyrozhdeniem besseleva tipa i kvaziklassicheskie asimptotiki”, Mat. zametki, 107:5 (2020), 780–786 | MR | Zbl
[16] Nazaikinskii V. E., “Kanonicheskii operator Maslova na lagranzhevykh mnogoobraziyakh v fazovom prostranstve, sootvetstvuyuschem vyrozhdayuschemusya na granitse volnovomu uravneniyu”, Mat. zametki, 96:2 (2014), 261–276 | Zbl
[17] Dobrokhotov S. Yu., Nazaikinskii V. E., “Efficient formulas for the Maslov canonical operator near a simple caustic”, Russ. J. Math. Phys., 25:4 (2018), 545–552 | DOI | MR | Zbl
[18] Anikin A. Yu., Dobrokhotov S. Yu., Nazaikinskii V. E., Tsvetkova A. V., “Ravnomernaya asimptotika v vide funktsii Eiri dlya kvaziklassicheskikh svyazannykh sostoyanii v odnomernykh i radialno-simmetrichnykh zadachakh”, Teor. i mat. fiz., 201:3 (2019), 382–414 | MR | Zbl
[19] Dobrokhotov S. Yu., Nazaikinskii V. E., “Ob asimptotike integrala tipa Besselya, imeyuschego prilozheniya v teorii nabega voln na bereg”, Mat. zametki, 102:6 (2017), 828–835 | Zbl
[20] Dobrokhotov S. Yu., Nazaikinskii V. E., “Nestandartnye lagranzhevy osobennosti i asimptoticheskie sobstvennye funktsii vyrozhdayuschegosya operatora $-\frac{d}{dx}D(x)\frac{d}{dx}$”, Tr. Mat. in-ta RAN, 306, 2019, 83–99 | Zbl
[21] Anikin A. Yu., Dobrokhotov S. Yu., Nazaikinskii V. E., “Prostye asimptotiki obobschennogo volnovogo uravneniya s vyrozhdayuscheisya skorostyu i ikh prilozheniya v lineinoi zadache o nabege dlinnykh voln na bereg”, Mat. zametki, 104:4 (2018), 483–504 | MR | Zbl
[22] Hewett D. P., Ockendon J. R., Smyshlyaev V. P., “Contour integral solutions of the parabolic wave equation”, Wave Motion, 84 (2019), 90–109 | DOI | MR | Zbl
[23] Anikin A. Yu., Dobrokhotov S. Yu., Nazaikinskii V. E., Tsvetkova A. V., “Asimptotiki sobstvennykh funktsii operatora $\nabla D(x) \nabla,$ svyazannye s bilyardami s poluzhestkimi stenkami, i zakhvachennye beregovye volny”, Mat. zametki, 105:5 (2019), 792–797 | MR | Zbl
[24] Anikin A. Yu., Dobrokhotov S. Yu., Nazaikinskii V. E., Tsvetkova A. V., “Asimptotiki sobstvennykh funktsii operatora $\nabla D(x) \nabla$ v dvumernoi oblasti, vyrozhdayuschegosya na ee granitse, i billiardy s poluzhestkimi stenkami”, Differ. uravn., 55:5 (2019), 660–672 | Zbl
[25] Anikin A. Yu., “Asimptotika odnomernykh lineinykh stoyachikh voln na vode s dispersiei i vyrozhdeniem na granitse”, Mat. zametki, 107:5 (2020), 774–779 | MR | Zbl
[26] Fedoryuk M. V., Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1983
[27] Babich V. M., “Matematicheskaya teoriya difraktsii (obzor nekotorykh issledovanii, vypolnennykh v laboratorii matematicheskikh problem geofiziki LOMI)”, Tr. Mat. in-ta AN SSSR, 175, 1986, 47–62 | Zbl
[28] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii, Nauka, M., 1989
[29] Slavyanov S. Yu., Asimptotika reshenii odnomernogo uravneniya Shredingera, Izd-vo Lenigr. un-ta, L., 1991
[30] Arnold V. I., “O kharakteristicheskom klasse, vkhodyaschem v usloviya kvantovaniya”, Funkts. anal. i ego pril., 1:1 (1967), 1–14 | Zbl
[31] Dobrokhotov S. Yu., Makrakis G., Nazaikinskii V. E., “Kanonicheskii operator Maslova, odna formula Khermandera i lokalizatsiya resheniya Berri–Balazha v teorii volnovykh puchkov”, Teor. i mat. fiz., 180:2 (2014), 162–188 | MR | Zbl
[32] Mischenko A. S., Sternin B. Yu., Shatalov V. E., Lagranzhevy mnogoobraziya i metod kanonicheskogo operatora, Nauka, M., 1978
[33] Dobrokhotov S. Yu., Nazaikinskii V. E., “Lagranzhevy mnogoobraziya i effektivnye formuly dlya korotkovolnovykh asimptotik v okrestnosti tochki vozvrata kaustiki”, Mat. zametki, 108:3 (2020), 334–359 | MR | Zbl