Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev—Petviashvili equation

doi:10.1088/1674-1056/ac1f08

中国物理B ›› 2022, Vol. 31 ›› Issue (3): 30201-030201.doi: 10.1088/1674-1056/ac1f08

• • 下一篇

Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev—Petviashvili equation

Jian-Wen Wu(吴剑文), Yue-Jin Cai(蔡跃进), and Ji Lin(林机)^†

Department of Physics, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2021-07-11 修回日期:2021-08-13 接受日期:2021-08-19 出版日期:2022-02-22 发布日期:2022-02-14
通讯作者: Ji Lin E-mail:linji@zjnu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11835011 and 12074343).

Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev—Petviashvili equation

Jian-Wen Wu(吴剑文), Yue-Jin Cai(蔡跃进), and Ji Lin(林机)^†

Department of Physics, Zhejiang Normal University, Jinhua 321004, China

Received:2021-07-11 Revised:2021-08-13 Accepted:2021-08-19 Online:2022-02-22 Published:2022-02-14
Contact: Ji Lin E-mail:linji@zjnu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11835011 and 12074343).

摘要/Abstract

摘要： With the aid of the Painlevé analysis, we obtain residual symmetries for a new (3+1)-dimensional generalized Kadomtsev—Petviashvili (gKP) equation. The residual symmetry is localized and the finite transformation is proposed by introducing suitable auxiliary variables. In addition, the interaction solutions of the (3+1)-dimensional gKP equation are constructed via the consistent Riccati expansion method. Particularly, some analytical soliton-cnoidal interaction solutions are discussed in graphical way.

关键词: residual symmetry, interaction solutions, (3+1)-dimensional generalized Kadomtsev—Petviashvili equation

Abstract: With the aid of the Painlevé analysis, we obtain residual symmetries for a new (3+1)-dimensional generalized Kadomtsev—Petviashvili (gKP) equation. The residual symmetry is localized and the finite transformation is proposed by introducing suitable auxiliary variables. In addition, the interaction solutions of the (3+1)-dimensional gKP equation are constructed via the consistent Riccati expansion method. Particularly, some analytical soliton-cnoidal interaction solutions are discussed in graphical way.

Key words: residual symmetry, interaction solutions, (3+1)-dimensional generalized Kadomtsev—Petviashvili equation

中图分类号: (Integrable systems)

02.30.Ik

05.45.Yv (Solitons) 04.20.Jb (Exact solutions)

Jian-Wen Wu(吴剑文), Yue-Jin Cai(蔡跃进), and Ji Lin(林机). Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev—Petviashvili equation[J]. 中国物理B, 2022, 31(3): 30201-030201.

参考文献

[1] Nayfeh A H and Hassan S D 1971 J. Fluid Mech. 48 463
[2] Kivshar Y S and Malomed B A 1989 Rev. Mod. Phys. 61 763
[3] Wang W, Yao R X and Lou S Y 2020 Chin. Phys. Lett. 37 100501
[4] Kamchatnov A M 1997 Phys. Rep. 286 199
[5] Leblond H and Mihalache D 2010 Phys. Rep. 523 61
[6] Wang B, Zhang Z and Li B 2020 Chin. Phys. Lett. 37 030501
[7] Nakamura Y and Tsukabayashi I 1984 Phys. Rev. Lett. 52 2356
[8] Shen Y, Tian B, Liu S H and Yang D Y 2021 Phys. Scripta 96 075212
[9] Jin X W and Lin J 2020 J. Magn. Magn. Mater. 514 167192
[10] Kartashov Y V and Konotop V V 2017 Phys. Rev. Lett. 118 190401
[11] Kadomtsev B B and Petviashvili V I 1970 Dokl. Akad. Nauk SSSR 192 753
[12] Zhang Z, Guo Q, Li B and Chen J C 2021 Commun. Nonlinear Sci. 101 105866
[13] Leblond H, Kremer D and Mihalache D 2010 Phys. Rev. A 81 033824
[14] Zhou Q 2022 Chin. Phys. Lett. 39 010501
[15] Lou S Y and Hu X B 1997 J. Math. Phys. 38 6401
[16] Oevel W and Fuchssteiner B 1982 Phys. Lett. A 88 323
[17] Ma W X 2020 Opt. Quantum Electron. 52 511
[18] Wang X B, Tian S F, Qin C Y and Zhang T T 2017 Appl. Math. Lett. 72 58
[19] Mao J J, Tian S F, Zou L and Zhang T T 2019 Nonlinear Dyn. 95 3005
[20] Guan X, Liu W J, Zhou Q and Biswas A 2020 Appl. Math. Comput. 366 124757
[21] Ma Y L, Wazwaz A M and Li B Q 2021 Math. Comput. Simul. 187 505
[22] Ma Y L, Wazwaz A M and Li B Q 2021 Nonlinear Dyn. 104 1581
[23] Ablowitz M J and Clarkson P A 1991 Solitons, nolinear evolution equations and inverse scattering (Cambridge:Cambridge University Press) 149
[24] Wang J, Su T, Geng X G and Li R M 2020 Nonlinear Dyn. 101 597
[25] Hirota R and Ito M 1981 J. Phys. Soc. Jpn. 50 338
[26] Ma W X, Yong X L and Lü X 2021 Wave Motion 103 102719
[27] Cai Y J, Wu J W, Hu L T and Lin J 2021 Phys. Scripta 96 095212
[28] Wang H F and Zhang Y F 2020 Chin. Phys. B 29 040501
[29] Liu Y K and Li B 2017 Chin. Phys. Lett. 34 010202
[30] Yin K H, Cheng X P and Lin J 2021 Chin. Phys. Lett. 38 080201
[31] Olver P J 1986 Applications of Lie groups to differential equations (New York:Springer-Verlag)
[32] Keane A J, Mushtaq A and Wheatland M S 2011 Phys. Rev. E 83 066407
[33] Kim E, Li F, Chong C, Theocharis G, Yang J and Kevrekidis P G 2015 Phys. Rev. Lett. 114 118002
[34] Feng L L, Tian S F and Zhang T T 2020 Bull. Malays. Math. Sci. Soc. 43 141
[35] Zhang Z, Qi Z Q and Li B 2021 Appl. Math. Lett. 116 107004
[36] Yang Y Q, Suzuki T and Wang J Y 2021 Commun. Nonlinear Sci. 95 105626
[37] Lou S Y, Hu X R and Chen Y 2012 J. Phys. A:Math. Theor. 45 155209
[38] Cheng X P, Chen C L and Lou S Y 2014 Wave Motion 51 1298
[39] Tang X Y, Hao X Z and Liang Z F 2017 Comput. Math. Appl. 74 1311
[40] Huang L L and Chen Y 2018 Nonlinear Dyn. 92 221
[41] Hu H C and Lu Y H 2020 Chin. Phys. B 29 040201
[42] Wu J W, Cai Y J and Lin J 2021 Commun. Theor. Phys. 73 065002
[43] Huang L L and Chen Y 2016 Chin. Phys. B 25 060201
[44] Hu H C, Hu X and Feng B F 2016 Z. Naturforsch. A 71 235
[45] Xia Y R, Xin X P and Zhang S L 2017 Chin. Phys. B 26 030202
[46] Hu X R and Chen Y 2015 Chin. Phys. B 24 090203
[47] Chen J C, Ma Z Y and Hu Y H 2017 Chin. Phys. Lett. 34 010201
[48] Liu P, Xu H R and Yang J R 2020 Acta Phys. Sin. 69 010203 (in Chinese)
[49] Ren B and Lin J 2020 Phys. Scripta 95 075202
[50] Ren B, Lin J and Lou Z M 2020 Appl. Math. Lett. 105 106326
[51] Hu X R, Lou S Y and Chen Y 2012 Phys. Rev. E 85 056607
[52] Tang X Y, Liang Z F and Wang J Y 2015 J. Phys. A:Math. Theor. 48 285204
[53] Lin J, Jin X W, Gao X L and Lou S Y 2018 Commun. Theor. Phys. 70 119
[54] Ren B 2017 Commun. Nonlinear Sci. 42 456
[55] Liu S J, Tang X Y and Lou S Y 2018 Chin. Phys. B 27 060201
[56] Wang X B, Jia M and Lou S Y 2021 Chin. Phys. B 30 010501
[57] Jin X W and Lin J 2020 J. Magn. Magn. Mater. 502 166590
[58] Bluman G W, Cheviakov A F and Anco S C 2010 Applications of symmetry methods to partial differential equations (New York:Springer)
[59] Lou S Y and Hu X B 1997 J. Phys. A:Math. Gen. 30 L95
[60] Cheng X P, Yang Y Q, Ren B and Wang J Y 2019 Wave Motion 86 150
[61] Bluman G W 2002 Symmetry and integration methods for differential equations (New York:Springer)
[62] Shin H J 2001 Phys. Rev. E 63 026606

Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev—Petviashvili equation

Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev—Petviashvili equation

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 6

Metrics

本文评价

推荐阅读 0

[1]	Yiyuan Zhang(张艺源), Ziqi Liu(刘子琪), Jiaxin Qi(齐家馨), and Hongli An(安红利). Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation[J]. 中国物理B, 2023, 32(3): 30505-030505.
[2]	夏亚荣, 辛祥鹏, 张顺利. Residual symmetry, interaction solutions, and conservation laws of the (2+1)-dimensional dispersive long-wave system[J]. 中国物理B, 2017, 26(3): 30202-030202.
[3]	刘希忠, 俞军, 任博. Explicit solutions from residual symmetry of the Boussinesq equation[J]. , 2015, 24(3): 30202-030202.
[4]	刘希忠, 俞军, 任博, 杨建荣. Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation[J]. , 2015, 24(1): 10203-010203.
[5]	刘希忠, 俞军, 任博, 杨建荣. Bäcklund transformations for the Burgers equation via localization of residual symmetries[J]. , 2014, 23(11): 110203-110203.
[6]	刘希忠, 俞军, 任博, 杨建荣. New interaction solutions of the Kadomtsev-Petviashvili equation[J]. , 2014, 23(10): 100201-100201.