Аннотация:
В работе дан новый вывод законов сохранения для уравнений длинных волн с помощью нелинейного интегрального уравнения и построен новый класс решений.
Образец цитирования:
Б. А. Купершмидт, Ю. И. Манин, “Уравнения длинных волн со свободной поверхностью. I. Законы сохранения и решения”, Функц. анализ и его прил., 11:3 (1977), 31–42; Funct. Anal. Appl., 11:3 (1977), 188–197
Keir Darling, Lawrence M Widrow, “Linear operator theory of phase mixing”, Monthly Notices of the Royal Astronomical Society, 533:1 (2024), 79
Frans H. van Eemeren, Rob Grootendorst, Handbook of Pragmatics, Handbook of Pragmatics, 2022, 82
Aleksandra Lelito, Oleg I. Morozov, “The Gibbons–Tsarev equation: symmetries, invariant solutions, and applications”, JNMP, 23:2 (2021), 243
Zakhar V. Makridin, Maxim V. Pavlov, “Multi‐dimensional conservation laws and integrable systems”, Stud Appl Math, 143:4 (2019), 339
З. В. Макридин, “Эффективный алгоритм нахождения многомерных законов сохранения для интегрируемых систем гидродинамического типа”, ТМФ, 194:2 (2018), 320–330; Z. V. Makridin, “An effective algorithm for finding multidimensional conservation laws for integrable systems of hydrodynamic type”, Theoret. and Math. Phys., 194:2 (2018), 274–283
Aleksandra Lelito, Oleg I. Morozov, “Invariant solutions to the Khokhlov-Zabolotskaya singular manifold equation and their application”, Reports on Mathematical Physics, 81:1 (2018), 65
Misha Bialy, Andrey E. Mironov, “In search of periodic solutions for a reduction of the Benney chain”, Journal of Mathematical Physics, 58:11 (2017)
Oleg I. Morozov, “Deformed cohomologies of symmetry pseudo-groups and coverings of differential equations”, Journal of Geometry and Physics, 113 (2017), 215
М. В. Павлов, Д. В. Прохоров, А. Ю. Васильев, А. М. Захаров, “Эволюция Лёвнера и конечномерные редукции интегрируемых систем”, ТМФ, 181:1 (2014), 155–172; M. V. Pavlov, D. V. Prokhorov, A. Yu. Vasiliev, A. M. Zaharov, “Löwner evolution and finite-dimensional reductions of integrable systems”, Theoret. and Math. Phys., 181:1 (2014), 1263–1278
Pavlov M.V., “Hamiltonian Formalism of Two-Dimensional Vlasov Kinetic Equation”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 470:2172 (2014), 20140343
Wei Fu, R. Ilangovane, K. M. Tamizhmani, Da-jun Zhang, “Integrability properties of the dispersionless Kadomtsev-Petviashvili hierarchy”, Journal of Mathematical Physics, 55:8 (2014)
P.G. Grinevich, P.M. Santini, “Holomorphic eigenfunctions of the vector field associated with the dispersionless Kadomtsev–Petviashvili equation”, Journal of Differential Equations, 255:7 (2013), 1469
Nicolas Besse, “On the Waterbag Continuum”, Arch Rational Mech Anal, 199:2 (2011), 453
А. В. Одесский, В. В. Соколов, “Интегрируемые (2+1)(2+1)-мерные системы гидродинамического типа”, ТМФ, 163:2 (2010), 179–221; A. V. Odesskii, V. V. Sokolov, “Integrable (2+1)(2+1)-dimensional systems of hydrodynamic type”, Theoret. and Math. Phys., 163:2 (2010), 549–586
Gibbons J., Lorenzoni P., Raimondo A., “Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type”, J Geom Phys, 60:9 (2010), 1112–1126
Yurii N. Grigoriev, Nail H. Ibragimov, Vladimir F. Kovalev, Sergey V. Meleshko, Lecture Notes in Physics, 806, Symmetries of Integro-Differential Equations, 2010, 57
Yurii N. Grigoriev, Nail H. Ibragimov, Vladimir F. Kovalev, Sergey V. Meleshko, Lecture Notes in Physics, 806, Symmetries of Integro-Differential Equations, 2010, 145
M England, J Gibbons, “A genus six cyclic tetragonal reduction of the Benney equations”, J. Phys. A: Math. Theor., 42:37 (2009), 375202
А. В. Одесский, М. В. Павлов, В. В. Соколов, “Классификация интегрируемых уравнений типа уравнения Власова”, ТМФ, 154:2 (2008), 249–260; A. V. Odesskii, M. V. Pavlov, V. V. Sokolov, “Classification of integrable Vlasov-type equations”, Theoret. and Math. Phys., 154:2 (2008), 209–219
Metin Gürses, Ismagil Habibullin, Kostyantyn Zheltukhin, “Hydrodynamic type integrable equations on a segment and a half-line”, Journal of Mathematical Physics, 49:10 (2008)
Цитирование в формате AMSBIB
Обратная связь: