Chin. Phys. Lett.  2024, Vol. 41 Issue (4): 040201    DOI: 10.1088/0256-307X/41/4/040201
GENERAL |
Some Modified Equations of the Sine-Hilbert Type
Ling-Juan Yan1,2, Ya-Jie Liu1,2*, and Xing-Biao Hu1,2
1LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
2School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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Ling-Juan Yan, Ya-Jie Liu, and Xing-Biao Hu 2024 Chin. Phys. Lett. 41 040201
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Abstract Three modified sine-Hilbert (sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided. Based on these bilinear equations, some exact solutions to the three modified equations are derived.
Received: 10 January 2024      Published: 12 April 2024
PACS:  02.30.Ik (Integrable systems)  
  02.60.Nm (Integral and integrodifferential equations)  
  05.45.Yv (Solitons)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/41/4/040201       OR      https://cpl.iphy.ac.cn/Y2024/V41/I4/040201
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Ling-Juan Yan
Ya-Jie Liu
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[1] Benjamin T B 1966 J. Fluid Mech. 25 241
[2] Davis R E and Acrivos A 1967 J. Fluid Mech. 29 593
[3] Ono H 1975 J. Phys. Soc. Jpn. 39 1082
[4] Joseph R I 1977 J. Phys. A 10 L225
[5] Kubota T, Ko D R S, and Dobbs L D 1978 J. Hydronautics 12 157
[6] Chen H H and Lee Y C 1979 Phys. Rev. Lett. 43 264
[7] Satsuma J, Ablowitz M J, and Kodama Y 1979 Phys. Lett. A 73 283
[8] Bock T L and Kruskal M D 1979 Phys. Lett. A 74 173
[9] Kodama Y, Satsuma J, and Ablowitz M J 1981 Phys. Rev. Lett. 46 687
[10] Santini P M, Ablowitz M J, and Fokas A S 1984 J. Math. Phys. 25 892
[11] Fokas A S and Ablowitz M J 1983 Stud. Appl. Math. 68 1
[12] Joseph R I and Egri R 1978 J. Phys. A 11 L97
[13] Matsuno Y 1979 J. Phys. A 12 619
[14] Miloh T 1990 J. Fluid Mech. 211 617
[15] Ablowitz M J, Fokas A S, Satsuma J, and Segur H 1982 J. Phys. A 15 781
[16] Satsuma J and Ishimori Y 1979 J. Phys. Soc. Jpn. 46 681
[17] Grimshaw R and Zhu Y 1994 Stud. Appl. Math. 92 249
[18] Matsuno Y 1980 J. Phys. A 13 1519
[19]Matsuno Y 1984 Bilinear Transformation Method (London: Academic Press)
[20]Ablowitz M A and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
[21] Klein C and Saut J C 2021 Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE (New York: Springer) p 97
[22] Degasperis A and Santini P M 1983 Phys. Lett. A 98 240
[23] Degasperis A, Santini P M, and Ablowitz M J 1985 J. Math. Phys. 26 2469
[24] Matsuno Y 2000 J. Math. Phys. 41 7061
[25] Peierls R 1940 Proc. Phys. Soc. 52 34
[26] Nabarro F R N 1947 Proc. Phys. Soc. 59 256
[27] Santini P M, Ablowitz M J, and Fokas A S 1987 J. Math. Phys. 28 2310
[28] Matsuno Y 1986 Phys. Lett. A 119 229
[29] Matsuno Y 1987 J. Phys. A 20 3587
[30] Matsumo Y 1987 Phys. Lett. A 120 187
[31] Matsuno Y 1992 J. Math. Phys. 33 3039
[32] Matsuno Y 1992 J. Math. Phys. 33 2754
[33] Matsuno Y 2008 J. Phys. A 42 025401
[34]Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
[35]King F W 2009 Hilbert Transforms (Cambridge: Cambridge University Press)
[36] Pöppe C 1983 Physica D 9 103
[37] Harada H 1985 J. Phys. Soc. Jpn. 54 4507
[38] Cooper F, Khare A, and Sukhatme U 2002 J. Phys. A 35 10085
[39] Khare A and Sukhatme U 2002 Phys. Rev. Lett. 88 244101. Jaworski M and Lakshmanan M 2003 Phys. Rev. Lett. 90 239401. Khare A and Sukhatme U 2003 Phys. Rev. Lett. 90 239402
[40] Ma W X and Fan E G 2011 Comput. & Math. Appl. 61 950
[41] Kodama Y 2018 CBMS-NSF Regional Conference Series in Applied Mathematics: Solitons in Two-Dimensional Shallow Water (Philadelphia, PA: SIAM Publications Library)
[42] Ma W X 2021 Commun. Theor. Phys. 73 065001
[43] Hao X Z and Lou S Y 2022 Math. Methods Appl. Sci. 45 5774
[44] Jia M and Lou S Y 2023 Phys. Scr. 98 105246
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