Geodesic
Soliton-like excitations in weakly dispersive media
Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 3, pp. 384-399 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the question of the possible existence of two-parameter envelope solitons in weakly dispersive media with an acoustic spectrum of linear waves. We propose an asymptotic procedure for finding such soliton solutions in the one-dimensional case and demonstrate the proposed method in the example of the modified Boussinesq equation. We study the question of nonlinear multidimensional localization of excitations in weakly dispersive media with an acoustic spectrum of linear waves.
Keywords: linear wave dispersion law, nonlinear wave, envelope soliton, Fourier series, power series expansion, asymptotic expansion. 
@article{TMF_2021_206_3_a5,
     author = {A. S. Kovalev},
     title = {Soliton-like excitations in weakly dispersive media},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {384--399},
     year = {2021},
     volume = {206},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_206_3_a5/}
}
TY  - JOUR
AU  - A. S. Kovalev
TI  - Soliton-like excitations in weakly dispersive media
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2021
SP  - 384
EP  - 399
VL  - 206
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2021_206_3_a5/
LA  - ru
ID  - TMF_2021_206_3_a5
ER  - 
%0 Journal Article
%A A. S. Kovalev
%T Soliton-like excitations in weakly dispersive media
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2021
%P 384-399
%V 206
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2021_206_3_a5/
%G ru
%F TMF_2021_206_3_a5
A. S. Kovalev. Soliton-like excitations in weakly dispersive media. Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 3, pp. 384-399. http://geodesic.mathdoc.fr/item/TMF_2021_206_3_a5/

[1] R. Dodd, Dzh. Eilbek, Dzh. Gibbon, Kh. Morris, Solitony i nelineinye volnovye uravneniya, Mir, M., 1988 | MR | Zbl

[2] A. Nyuell, Solitony v matematike i fizike, Mir, M., 1989 | MR

[3] Yu. S. Kivshar, G. P. Agraval, Opticheskie solitony. Ot volokonnykh svetovodov k fotonnym kristallam, Fizmatlit, M., 2005

[4] O. A. Sulymenko, O. V. Prokopenko, V. S. Teberkevych, A. V. Slavin, A. A. Serga, “Bullets and droplets: Two-dimensional spin-wave solitons in modern magnonics (Review article)”, FNT, 44:7 (2018), 775–793 | DOI

[5] N. Manton, P. Sutcliff, Topological Solitons, Cambridge Univ. Press, Cambridge, 2004 | DOI | MR

[6] V. M. Eleonskii, V. P. Silin, “Teoriya voln, blizkikh k tochnym resheniyam nelineinoi elektrodinamiki i optiki. I”, ZhETF, 56:2 (1969), 574–591; “Теория волн, близких к точным решениям нелинейной электродинамики и оптики. II”, 57:2 (1970), 478–488

[7] V. M. Eleonskii, V. P. Silin, “Teoriya yavleniya samokanalizatsii elektromagnitnogo polya v nelineinoi srede”, ZhETF, 58:5 (1970), 1715–1726

[8] A. M. Kosevich, A. S. Kovalev, “Samolokalizatsiya kolebanii v odnomernoi angarmonicheskoi tsepochke”, ZhETF, 67:5 (1974), 1793–1804

[9] V. M. Eleonskii, N. E. Kulagin, N. S. Novozhilova, V. P. Silin, “O samolokalizovannykh v prostranstve i periodicheskikh vo vremeni resheniyakh volnovykh uravnenii”, Metody kachestvennoi teorii differentsialnykh uravnenii, Izd-vo GGU, Gorkii, 1982, 73–92

[10] V. M. Eleonskii, N. E. Kulagin, N. S. Novozhilova, V. P. Silin, Metod asiptoticheskikh razlozhenii i kachestvennyi analiz konechnomernykh modelei v teorii nelineinogo polya, Preprint FIAN SSSR No 272, FIAN, M., 1983

[11] N. N. Bogolyubov, Yu. A. Mitropolskii, Asimptoticheskie metody v teorii nelineinykh kolebanii, Fizmatgiz, M., 1963 | MR | MR

[12] N. N. Moiseev, Asimptoticheskie metody nelineinoi mekhaniki, Nauka, M., 1969 | MR | Zbl

[13] A. Naife, Vvedenie v metody vozmuschenii, Mir, M., 1984 | MR | Zbl

[14] Dzh. Uizem, Lineinye i nelineinye volny, Mir, M., 1977 | MR | MR | Zbl

[15] N. N. Akhmediev, A. Ankevich, Solitony, Fizmatlit, M., 2003

[16] A. M. Kosevich, A. S. Kovalev, Vvedenie v nelineinuyu fizicheskuyu mekhaniku, Naukova dumka, Kiev, 1989

[17] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov. Metod obratnoi zadachi, Nauka, M., 1980 | MR | Zbl

[18] V. E. Zakharov, A. B. Shabat, “Tochnaya teoriya dvumernoi samofokusirovki i odnomernoi avtomodulyatsii voln v nelineinoi srede”, ZhETF, 61:1 (1971), 118–134 | MR

[19] V. E. Zakharov, “O stokhastizatsii v odnomernykh tsepochkakh nelineinykh ostsillyatorov”, ZhETF, 65:1 (1973), 219–225

[20] C. S. Gardner, J. P. Greene, M. D. Kruskal, K. M. Miura, “Method for solving the Korteweg–deVries equation”, Phys. Rev. Lett., 19:19 (1967), 1095–1097 | DOI

[21] M. Tajiri, Y. Murakami, “On breather solutions to the Boussinesq equation”, J. Phys. Soc. Japan, 58:10 (1989), 3585–3590 | DOI | MR

[22] G. E. Fal'kovich, M. D. Spector, S. K. Turitsyn, “Distraction of stationary solutions and collapse in the nonlinear string equation”, Phys. Lett. A, 99:6–7 (1983), 271–274 | DOI | MR

[23] V. K. Kolontarov, O. A. Ladyzhenskaya, “O vozniknovenii kollapsov dlya kvazilineinykh uravnenii parabolicheskogo i giperbolicheskogo tipov”, Zap. nauchn. sem. LOMI, 69 (1977), 77–102 | DOI | MR | Zbl

[24] A. S. Kovalev, E. S. Syrkin, “Vliyanie prostranstvennoi dispersii i kapillyarnykh effektov na rasprostranenie i zatukhanie nelineinykh poverkhnostnykh voln”, ZhETF, 102:2 (1992), 522–533

[25] A. S. Kovalev, E. S. Syrkin, Zh. A. Mozhen, “Mnogomernye i poverkhnostnye solitony v nelineinykh uprugikh sredakh”, FNT, 28:6 (2002), 635–647 | DOI

[26] A. A. Maradudin, “Surface acoustic waves on real surfaces”, Physics of Phonons, Lecture Notes in Physics, 285, ed. T. Paszkiewicz, Springer, Berlin, 1987, 82–147 | DOI

[27] R. Y. Chiao, E. Garmire, C. H. Townes, “Self-trapping of optical beams”, Phys. Rev. Lett., 13:15 (1964), 479–482 | DOI