Mots-clés : Hirota equation
@article{TMF_2023_214_1_a1,
author = {U. A. Khoitmetov},
title = {Integration of the {Hirota} equation with time-dependent coefficients},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {30--42},
year = {2023},
volume = {214},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2023_214_1_a1/}
}
U. A. Khoitmetov. Integration of the Hirota equation with time-dependent coefficients. Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 1, pp. 30-42. http://geodesic.mathdoc.fr/item/TMF_2023_214_1_a1/
[1] K. U. Tariq, M. Younis, H. Rezazadeh, S. T. R. Rizvi, M. S. Osman, “Optical solitons with quadratic–cubic nonlinearity and fractional temporal evolution”, Modern Phys. Lett. B, 32:26 (2018), 1850317, 13 pp. | DOI | MR
[2] M. S. Osman, “One-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient Sawada–Kotera equation”, Nonlinear Dynam., 96:2 (2019), 1491–1496 | DOI
[3] M. S. Osman, K. U. Tariq, A. Bekir, A. Elmoasry, N. S. Elazab, M. Younis, M. Abdel-Aty, “Investigation of soliton solutions with different wave structures to the $(2+1)$-dimensional Heisenberg ferromagnetic spin chain equation”, Commun. Theor. Phys., 72:3 (2020), 035002, 7 pp. | DOI | MR
[4] D. Lu, K. U. Tariq, M. S. Osman, D. Baleanu, M. Younis, M. M. A. Khater, “New analytical wave structures for the $(3+1)$-dimensional Kadomtsev–Petviashvili and the generalized Boussinesq models and their applications”, Results Phys., 14 (2019), 102491, 7 pp. | DOI
[5] A. R. Seadawy, “Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma”, Phys. A, 439 (2015), 124–131 | DOI | MR
[6] A.-M. Wazwaz, “Multiple complex soliton solutions for integrable negative-order KdV and integrable negative-order modified KdV equations”, Appl. Math. Lett., 88 (2019), 1–7 | DOI | MR
[7] K. S. Al-Ghafri, H. Rezazadeh, “Solitons and other solutions of $(3+1)$-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov equation”, Appl. Math. Nonlinear Sci., 4:2 (2019), 289–304 | MR
[8] A.-M. Wazwaz, “A $(2+1)$-dimensional time-dependent Date–Jimbo–Kashiwara–Miwa equation: Painlevé integrability and multiple soliton solutions”, Comput. Math. Appl., 79:4 (2020), 1145–1149 | DOI | MR
[9] D. W. Brzezinski, “Review of numerical methods for NumILPT with computational accuracy assessment for fractional calculus”, App. Math. Nonlinear Sci., 3:2 (2018), 487–502 | MR
[10] R. Hirota, “Exact envelope-soliton solutions of a nonlinear wave equation”, J. Math. Phys., 14:7 (1973), 805–809 | DOI | MR
[11] R. Hirota, The Direct Method in Soliton Theory, Cambridge Tracts in Mathematics, 155, Cambridge Univ. Press, Cambridge, 2004 | DOI | MR
[12] Y. Fukumoto, T. Miyazaki, “Three-dimensional distortions of a vortex filament with axial velocity”, J. Fluid Mech., 222 (1991), 369–416 | DOI | MR
[13] M. Eslami, M. A. Mirzazadeh, A. Neirameh, “New exact wave solutions for Hirota equation”, Pramana – J. Phys., 84:1 (2015), 3–8 | DOI
[14] J. Cen, F. Correa, A. Fring, “Integrable nonlocal Hirota equations”, J. Math. Phys., 60:8 (2019), 081508 | DOI | MR
[15] Q. Wang, Y. Chen, B. Li, H.-Q. Zhang, “New exact travelling wave solutions to Hirota equation and $(1+1)$-dimensional dispersive long wave equation”, Commun. Theor. Phys., 41:6 (2004), 821–828 | DOI | MR
[16] A. A. Al Qarni, A. A. Alshaery, H. O. Bakodah, J. F. Gómez-Aguilar, “Novel dynamical solitons for the evolution of Schrödinger–Hirota equation in optical fibres”, Opt. Quant. Electron., 53 (2021), 151, 15 pp. | DOI
[17] X. Zhang, L. Ling, “Asymptotic analysis of high-order solitons for the Hirota equation”, Phys. D, 426 (2021), 132982, 26 pp. | DOI | MR
[18] A. Ankiewicz, J. M. Soto-Crespo, N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation”, Phys. Rev. E, 81:4 (2010), 046602, 8 pp. | DOI | MR
[19] S. Chen, Z. Yan, “The Hirota equation: Darboux transform of the Riemann–Hilbert problem and higher-order rogue waves”, App. Math. Lett., 95 (2019), 65–71 | DOI | MR
[20] F. Demontis, G. Ortenzi, C. van der Mee, “Exact solutions of the Hirota equation and vortex filaments motion”, Phys. D, 313 (2015), 61–80 | DOI | MR
[21] Y. Li, S.-F. Tian, “Inverse scattering transform and soliton solutions of an integrable nonlocal Hirota equation”, Commun. Pure Appl. Anal., 21:1 (2022), 293–313 | DOI
[22] Y. Tao, J. He, “Multisolitons, breathers, and rogue waves for the Hirota equation generated by the Darboux transformation”, Phys. Rev. E, 85:2 (2012), 026601, 7 pp. | DOI
[23] M. Ablovits, Kh. Sigur, Solitony i metod obratnoi zadachi, Mir, M., 1987 | MR | MR | Zbl | Zbl
[24] R. Dodd, Dzh. Eilbek, Dzh. Gibbon, Kh. Morris, Solitony i nelineinye volnovye uravneniya, Mir, M., 1988 | MR | MR | Zbl
[25] L. A. Takhtadzhyan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | DOI | MR | MR | Zbl
[26] C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura, “Method for solving the Korteweg–de Vries equation”, Phys. Rev. Lett., 19:19 (1967), 1095–1097 | DOI
[27] V. E. Zakharov, A. B. Shabat, “Tochnaya teoriya dvumernoi samofokusirovki v odnomernoi avtomodulyatsii voln v nelineinykh sredakh”, ZhETF, 61:1 (1971), 118–134 | MR
[28] M. Wadati, “The exact solution of the modified Korteweg–de Vries equation”, J. Phys. Soc. Japan, 32:6 (1972), 1681–1681 | DOI
[29] P. D. Lax, “Integrals of nonlinear equations of evolution and solitary waves”, Comm. Pure Appl. Math., 21:5 (1968), 467–490 | DOI | MR
[30] A. B. Khasanov, U. A. Khoitmetov, “Ob integrirovanii uravneniya Kortevega–de Friza v klasse bystroubyvayuschikh kompleksnoznachnykh funktsii”, Izv. vuzov. Matem., 2018, no. 3, 79–90 | DOI | Zbl
[31] V. E. Zakharov, L. A. Takhtadzhyan, L. D. Faddeev, “Polnoe opisanie reshenii ‘sin-Gordon’ uravneniya”, Dokl. AN SSSR, 219:6 (1974), 1334–1337 | MR | Zbl
[32] F. Demontis, “Tochnye resheniya modifitsirovannogo uravneniya Kortevega–de Friza”, TMF, 168:1 (2011), 35–48 | DOI | DOI | MR
[33] G. U. Urazboev, U. A. Khoitmetov, A. K. Babadzhanova, “Integrirovanie matrichnogo modifitsirovannogo uravneniya Kortevega–de Friza s istochnikom integralnogo tipa”, TMF, 203:3 (2020), 351–364 | DOI | DOI | MR
[34] R. Camassa, D. D. Holm, “An integrable shallow water equation with peaked solitons”, Phys. Rev. Lett., 71:11 (1993), 1661–1664, arXiv: patt-sol/9305002 | DOI | MR
[35] I. S. Frolov, “Obratnaya zadacha rasseyaniya dlya sistemy Diraka na vsei osi”, Dokl. AN SSSR, 207:1 (1972), 44–47 | MR | Zbl
[36] A. B. Khasanov, “Ob obratnoi zadachi teorii rasseyaniya dlya sistemy dvukh nesamosopryazhennykh differentsialnykh uravnenii pervogo poryadka”, Dokl. AN SSSR, 277:3 (1984), 559–562 | MR | Zbl
[37] A. M. Nakhushev, “Nagruzhennye uravneniya i ikh prilozheniya”, Differents. uravneniya, 19:1 (1983), 86–94 | MR
[38] A. M. Nakhushev, Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995
[39] A. I. Kozhanov, “Nelineinye nagruzhennye uravneniya i obratnye zadachi”, Zh. vychisl. matem. i matem. fiz., 44:4 (2004), 694–716 | MR | Zbl
[40] A. B. Hasanov, U. A. Hoitmetov, “On integration of the loaded Korteweg–de Vries equation in the class of rapidly decreasing functions”, Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan, 47:2 (2021), 250–261 | DOI | MR
[41] U. A. Khoitmetov, “Integrirovanie nagruzhennogo uravneniya KdF s samosoglasovannym istochnikom integralnogo tipa v klasse bystroubyvayuschikh kompleksnoznachnykh funktsii”, Matem. tr., 24:2 (2021), 181–198 | DOI | DOI
[42] A. B. Khasanov, U. A. Hoitmetov, “On integration of the loaded mKdV equation in the class of rapidly decreasing functions”, Izv. Irkut. gos. un-ta. Ser. Matem., 38 (2021), 19–35 | DOI | MR
[43] A. B. Khasanov, U. A. Khoitmetov, “Integrirovanie obschego nagruzhennogo uravneniya Kortevega–de Friza s integralnym istochnikom v klasse bystroubyvayuschikh kompleksnoznachnykh funktsii”, Izv. vuzov. Matem., 2021, no. 7, 52–66 | DOI
[44] A. B. Khasanov, U. A. Khoitmetov, “O kompleksnoznachnykh resheniyakh obschego nagruzhennogo uravneniya Kortevega–de Friza s istochnikom”, Differents. uravneniya, 58:3 (2022), 385–394 | DOI | DOI
[45] A. B. Khasanov, T. G. Khasanov, “Integrirovanie nelineinogo uravneniya Kortevega–de Friza s nagruzhennym chlenom i istochnikom”, Sib. zhurn. industr. matem., 25:2 (2022), 127–142 | MR
[46] U. A. Hoitmetov, “Integration of the loaded general Korteweg–de Vries equation in the class of rapidly decreasing complex-valued functions”, Eurasian Math. J., 13:2 (2022), 43–54 | DOI | MR