Mots-clés : soliton.
@article{TMF_2021_206_2_a3,
author = {Hui Mao},
title = {Novikov equation: {B\"acklund} transformation and applications},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {186--198},
year = {2021},
volume = {206},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2021_206_2_a3/}
}
Hui Mao. Novikov equation: Bäcklund transformation and applications. Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 2, pp. 186-198. http://geodesic.mathdoc.fr/item/TMF_2021_206_2_a3/
[1] V. Novikov, “Generalizations of the Camassa–Holm equation”, J. Phys. A: Math. Theor., 42:34 (2009), 342002, 14 pp. | DOI | MR
[2] A. N. W. Hone, J. P. Wang, “Integrable peakon equations with cubic nonlinearity”, J. Phys. A: Math. Theor., 41:37 (2008), 372002, 10 pp. | DOI | MR
[3] 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
[4] A. N. W. Hone, H. Lundmark, J. Szmigielski, “Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa–Holm type equation”, Dyn. Partial Differ. Equ., 6:3 (2009), 253–289 | DOI | MR
[5] Y. Matsuno, “Smooth multisoliton solutions and their peakon limit of Novikov's Camassa–Holm type equation with cubic nonlinearity”, J. Phys. A: Math. Theor., 46:36 (2013), 365203, 27 pp. | DOI | MR
[6] L. Wu, C. Li, N. Li, “Soliton solutions to the Novikov equation and a negative flow of the Novikov hierarchy”, Appl. Math. Lett., 87 (2019), 134–140 | DOI | MR
[7] C. Rogers, W. F. Shadwick, Bäcklund Transformations and Their Applications, Mathematics in Science and Engineering, 161, Academic Press, New York–London, 1982 | MR
[8] C. Rogers, W. Schief, Bäcklund and Darboux Transformations. Geometry and Modern Applications in Soliton Theory, Cambridge Texts in Applied Mathematics, 30, Cambridge Univ. Press, Cambridge, 2002 | DOI | MR
[9] C. Gu, H. Hu, Z. Zhou, Darboux Transformation in Soliton Theory and its Geometric Applications, Shanghai Scientific and Technical Press, Shanghai, 2005
[10] J. Hietarinta, N. Joshi, F. W. Nijhoff, Discrete Systems and Integrability, Cambridge Texts in Applied Mathematics, 54, Cambridge Univ. Press, Cambridge, 2016 | DOI | MR
[11] Y. B. Suris, The Problem of Integrable Discretization: Hamiltonian Approach, Progress in Mathematics, 219, Birkhäuser, Basel, 2003 | DOI | MR
[12] D. Levi, R. Benguria, “Bäcklund transformations and nonlinear differential difference equations”, Proc. Nat. Acad. Sci. USA, 77:9 (1980), 5025–5027 | DOI | MR
[13] D. Levi, “Nonlinear differential difference equations as Bäcklund transformations”, J. Phys. A: Math. Gen., 14:5 (1981), 1083–1098 | DOI | MR
[14] A. G. Rasin, J. Schiff, “The Gardner method for symmetries”, J. Phys. A: Math. Theor., 46:15 (2013), 155202, 15 pp. | DOI | MR | Zbl
[15] A. G. Rasin, J. Schiff, “Bäcklund transformations for the Camassa–Holm equation”, J. Nonlinear Sci., 27:1 (2017), 45–69 | DOI | MR
[16] G. Wang, Q. P. Liu, H. Mao, “The modified Camassa–Holm equation: Bäcklund transformations and nonlinear superposition formula”, J. Phys. A: Math. Theor., 53:29 (2020), 294003, 15 pp. | DOI | MR
[17] Khuei Mao, Gai-Khua Van, “Preobrazovanie Beklunda dlya uravneniya Degasperisa–Prochezi”, TMF, 203:3 (2020), 365–379 | DOI | DOI
[18] A. G. Rasin, J. Schiff, “A simple-looking relative of the Novikov, Hirota–Satsuma and Sawada–Kotera equations”, J. Nonlinear Math. Phys., 26:4 (2019), 555–568 | DOI | MR
[19] C. Rogers, P. Wong, “On reciprocal Bäcklund transformations of inverse scattering schemes”, Phys. Scr., 30:1 (1984), 10–14 | DOI | MR