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Chin. Phys. B, 2023, Vol. 32(4): 040503    DOI: 10.1088/1674-1056/ac9de6
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Lie symmetry analysis and invariant solutions for the (3+1)-dimensional Virasoro integrable model

Hengchun Hu(胡恒春) and Yaqi Li(李雅琦)
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract  Lie symmetry analysis is applied to a (3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators. Invariant solutions with arbitrary functions for the (3+1)-dimensional Virasoro integrable model, including the interaction solution between a kink and a soliton, the lump-type solution and periodic solutions, have been studied analytically and graphically.
Keywords:  (3+1)-dimensional Virasoro integrable model      Lie symmetry      invariant solutions  
Received:  18 September 2022      Revised:  13 October 2022      Accepted manuscript online:  27 October 2022
PACS:  05.45.Yv (Solitons)  
  02.30.Ik (Integrable systems)  
Corresponding Authors:  Hengchun Hu     E-mail:

Cite this article: 

Hengchun Hu(胡恒春) and Yaqi Li(李雅琦) Lie symmetry analysis and invariant solutions for the (3+1)-dimensional Virasoro integrable model 2023 Chin. Phys. B 32 040503

[1] Matveev V B and Salle M A 1990 Darboux Transformations and Solitons (Berlin: Springer-Verlag) p. 70
[2] Bluman G W and Kumei S 1989 Symmetries and Differential Equations (New York: Springer) p. 195
[3] Weiss J, Tabor M and Carnevale G 1983 J. Math. Phys. 24 522
[4] Lou S Y and Hu X B 1997 J. Phys. A: Math. Gen. 30 L95
[5] Jia J and Lin J 2012 Opt. Express 20 7469
[6] Lin J, Ren B, Li H M and Li Y S 2008 Phys. Rev. E 77 036605
[7] Hu H C, Li Y Y and Zhu H D 2018 Chaos Soliton. Fract. 108 77
[8] Hu H C and Li X D 2022 Int. J. Mod. Phys. B 36 2250001
[9] Kumar S, Kumar D and Kumar A 2020 Chaos Soliton. Fract. 142 110507
[10] Chen J C, Ma Z Y and Hu Y H 2018 J. Math. Anal. Appl. 460 987
[11] Chen J C and Zhu S D 2017 Appl. Math. Lett. 73 136
[12] Hu H C and Sun R L 2022 Mod. Phys. Lett. B 36 2150587
[13] Hu H C and Zhang Y Q 2021 Mod. Phys. Lett. B 35 2150108
[14] Hu H C and Liu F Y 2020 Chin. Phys. B 29 040201
[15] Huang L 2006 Acta Phys. Sin. 55 3864 (in Chinese)
[16] Lin J and Wang K L 2001 Acta Phys. Sin. 50 13 (in Chinese)
[17] Zhang H Y and Ran Z 2009 Chin. Phys. Lett. 26 030203
[18] Lin J 1996 Commun. Theor. Phys. 25 447
[19] Lin J, Lou S Y and Wang K L 2001 Phys. Lett. A 287 257
[20] Lin J, Lou S Y and Wang K L 2000 Z. Naturforsch. A 55 589
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