Geodesic
Influence of weak nonlinearity on the high-frequency asymptotics in caustic rearrangements
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 2, pp. 197-206 Cet article a éte moissonné depuis la source Math-Net.Ru

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A study is made of the influence of weak nonlinearity on the structure of the high-frequency asymptotics in the neighborhood of singular points of caustics. The properties of the resulting nonlinear analogs of the special functions of wave catastrophes are described. It is shown that these nonlinear special functions satisfy ordinary differential equations. 
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     author = {B. I. Suleimanov},
     title = {Influence of weak nonlinearity on the high-frequency asymptotics in caustic rearrangements},
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B. I. Suleimanov. Influence of weak nonlinearity on the high-frequency asymptotics in caustic rearrangements. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 2, pp. 197-206. http://geodesic.mathdoc.fr/item/TMF_1994_98_2_a2/

[1] Maslov V. P., Fedoryuk M. V., Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 | MR

[2] Babich V. M., Buldyrev B. C., Asimptoticheskie metody v zadachakh difraktsii korotkikh voln, Nauka, M., 1972 | MR

[3] Babich V. M., Kirpichnikova N. Ya., Metod pogranichnogo sloya v zadachakh difraktsii, LGU, Leningrad, 1974 | MR

[4] Fedoryuk M. V., Asimptotika, integraly i ryady, Nauka, M., 1987 | MR

[5] Arnold V. I., Funkts. analiz i ego prilozh., 6:4 (1972), 3–25 | MR | Zbl

[6] Vinogradova M. B., Rudenko O. V., Sukhorukov A. P., Teoriya voln, Nauka, M., 1979 | MR

[7] Peregrin D. H., Smith R., Trans. Roy. Soc. London. Ser. A, 292 (1979), 341–370 | DOI | Zbl

[8] Garnier R., Ann. scient. Norm. Super, 29 (1912), 1–313 | DOI | MR

[9] Jimbo M., Publ. RIMS, Kyoto Univ., 18:3 (1982), 1137–1161 | DOI | MR | Zbl

[10] Novokshenov V. Yu., Funkts. analiz i ego prilozh., 18:1 (1984), 90–91 | MR | Zbl

[11] Novokshenov V. Yu., Suleimanov B. I., UMN, 39:4 (1984), 114–115

[12] Suleimanov B. I., Diff. uravneniya, 23:5 (1987), 834–842 | MR | Zbl

[13] Its A. R., Kapaev A. A., Izv. AN SSSR. Ser. matem., 51:4 (1987), 878–892 | MR | Zbl

[14] Suleimanov B. I., Zadachi matematicheskoi fiziki i asimptotika ikh reshenii, Ufa, 1991, 33–49

[15] Its A. R., Izv. AN SSSR. Ser. matem., 49:3 (1985), 530–565 | MR | Zbl

[16] Kitaev A. V., Zap. nauchn. semin. LOMI, 187, 1991, 53–74 | MR

[17] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[18] Arnold V. I., Teoriya katastrof, Nauka, M., 1989 | MR

[19] Manukyan S. M., Prikl. matem. i mekh., 45:1 (1981), 95–105 | MR

[20] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR

[21] Haberman R., Sun R., Stud. Appl. Math., LXII:1 (1985), 1–38 | DOI | MR

[22] Zakharov V. E., Shabat A. B., ZhETF, 61:1 (1972), 118–134 | MR

[23] Suleimanov B. I., Dokl. RAN, 326:1 (1992), 40–44 | MR | Zbl

[24] Poston T., Styuart I., Teoriya katastrof i ee prilozheniya, Mir, M., 1980 | MR | Zbl

[25] Vazov V., Asimptoticheskie razlozheniya reshenii obyknovennykh differentsialnykh uravnenii, Mir, M., 1988

[26] Orlov A. Yu., Shulman V. I., TMF, 64:2 (1985), 323–328 | MR | Zbl

[27] Krichever I. M., Funkts. analiz i ego prilozh., 14:3 (1980), 83–84 | MR | Zbl

[28] Zhiber A. V., Dinamika sploshnoi sredy, 1980, no. 44, 3–14 | MR | Zbl