Localized wave solutions and interactions of the (2+1)-dimensional Hirota—Satsuma—Ito equation

doi:10.1088/1674-1056/ad1f4c

中国物理B ›› 2024, Vol. 33 ›› Issue (4): 40505-040505.doi: 10.1088/1674-1056/ad1f4c

Localized wave solutions and interactions of the (2+1)-dimensional Hirota—Satsuma—Ito equation

Qiankun Gong(巩乾坤), Hui Wang(王惠)^†, and Yunhu Wang(王云虎)

School of Science, Shanghai Maritime University, Shanghai 201306, China

收稿日期:2023-12-02 修回日期:2024-01-14 接受日期:2024-01-17 出版日期:2024-03-19 发布日期:2024-04-01
通讯作者: Hui Wang E-mail:hwang@shmtu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12275172 and 11905124).

Localized wave solutions and interactions of the (2+1)-dimensional Hirota—Satsuma—Ito equation

Qiankun Gong(巩乾坤), Hui Wang(王惠)^†, and Yunhu Wang(王云虎)

School of Science, Shanghai Maritime University, Shanghai 201306, China

Received:2023-12-02 Revised:2024-01-14 Accepted:2024-01-17 Online:2024-03-19 Published:2024-04-01
Contact: Hui Wang E-mail:hwang@shmtu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12275172 and 11905124).

摘要/Abstract

摘要： This paper studies the (2+1)-dimensional Hirota—Satsuma—Ito equation. Based on an associated Hirota bilinear form, lump-type solution, two types of interaction solutions, and breather wave solution of the (2+1)-dimensional Hirota—Satsuma—Ito equation are obtained, which are all related to the seed solution of the equation. It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons, and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton. Furthermore, the breather wave solution is also obtained by reducing the two-soliton solutions. The trajectory and period of the one-order breather wave are analyzed. The corresponding dynamical characteristics are demonstrated by the graphs.

关键词: lump solution, rogue wave solution, breather wave solution, (2+1)-dimensional Hirota—Satsuma—Ito equation

Abstract: This paper studies the (2+1)-dimensional Hirota—Satsuma—Ito equation. Based on an associated Hirota bilinear form, lump-type solution, two types of interaction solutions, and breather wave solution of the (2+1)-dimensional Hirota—Satsuma—Ito equation are obtained, which are all related to the seed solution of the equation. It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons, and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton. Furthermore, the breather wave solution is also obtained by reducing the two-soliton solutions. The trajectory and period of the one-order breather wave are analyzed. The corresponding dynamical characteristics are demonstrated by the graphs.

Key words: lump solution, rogue wave solution, breather wave solution, (2+1)-dimensional Hirota—Satsuma—Ito equation

中图分类号: (Solitons)

05.45.Yv

02.30.Ik (Integrable systems) 02.30.Jr (Partial differential equations)

Qiankun Gong(巩乾坤), Hui Wang(王惠), and Yunhu Wang(王云虎). Localized wave solutions and interactions of the (2+1)-dimensional Hirota—Satsuma—Ito equation[J]. 中国物理B, 2024, 33(4): 40505-040505.

Qiankun Gong(巩乾坤), Hui Wang(王惠), and Yunhu Wang(王云虎). Localized wave solutions and interactions of the (2+1)-dimensional Hirota—Satsuma—Ito equation[J]. Chin. Phys. B, 2024, 33(4): 40505-040505.

参考文献

[1] Chorin A J 1968 Math. Comput. 22 745
[2] Constantin P and Foias C 1988 Navier-Stokes Equations, 2nd edn. (Chicago:Chicago University Press)
[3] Galdi G 2011 An Introduction to the Mathematical Theory of the Navier-Stokes Equations:Steady-State Problems (Luxembourg:Springer)
[4] Grue J, Jensen A, Rusaas P O and Sveen J K 1999 J. Fluid Mech. 380 257
[5] Koop C G and Butler G 1981 J. Fluid Mech. 112 225
[6] Michallet H and Barthelemy E 1998 J. Fluid Mech. 366 159
[7] Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240
[8] Osman M S, Liu J G, Hosseini K, Lnc M and Yusuf A 2020 Phys. Scr. 95 035229
[9] Zhang W X and Liu Y Q 2021 AIMS Math. 6 11046
[10] Zahran E H M and Bekir A 2022 Chin. J. Phys. 77 1236
[11] Zhang W X and Liu Y Q 2022 Nonlinear Dyn. 108 2531
[12] Guo L J, Chen L, Mihalache D and He J S 2022 Phys. Rev. E 105 014218
[13] Akinyemi L, Senol M, Tasbozan O and Kurt A 2022 J. Ocean Eng. Sci. 7 536
[14] Zeng S J, Liu Y Q, Chen X and Zhang W X 2022 Results Phys. 42 105992
[15] Chen M and Wang Z 2023 Chin. Phys. B 32 090504
[16] Ablowitz M J and Satsuma J 1978 J. Math. Phys. 19 2180
[17] Umeki M 1997 Phys. Lett. A 236 69
[18] Yuan F, He J S and Cheng Y 2020 Commun. Nonlinear Sci. Numer. Simul. 83 105027
[19] Zhao Z L and He L C 2021 Appl. Math. Lett. 111 106612[RefAutoNo] Vladimir I Kruglov and Houria Triki 2023 Chin. Phys. Lett. 40 090503
[20] Ma W X 2015 Phys. Lett. A 379 1975
[21] Wang H, Tian S F, Zhang T T and Chen Y 2019 Front. Math. China 14 631
[22] Ismael H F, Murad M A S and Bulut H 2022 Chin. J. Phys. 77 1357
[23] Zhang Z, Yang X, Li B, Guo Q and Stepanyants Y 2023 Nonlinear Dyn. 111 1625
[24] Ma H C, Mao X and Deng A P 2023 Chin. Phys. B 32 060201
[25] Zhang X E and Chen Y 2017 Nonlinear Dyn. 90 755
[26] Liu J G and Zhao H 2022 Chin. J. Phys. 77 985
[27] Chen J C and Zhu S D 2017 Appl. Math. Lett. 73 136
[28] Chen J C, Ma Z Y and Hu Y H 2018 J. Math. Anal. Appl. 460 987
[29] Kundu A, Mukherjee A and Naskar T 2014 Proc. R. Soc. A 470 20130576
[30] Deng G F, Gao Y T, Ding C C and Su J J 2020 Chaos, Solitons and Fractals 140 110085
[31] Hirota R 2004 The Direct Method in Soliton Theory (Cambridge:Cambridge University Press)
[32] Matveev V B and Salle M A 1991 Darboux Transformation and Solitons (Berlin:Springer-Verlag)
[33] Ablowitz M J, Kaup D J, Newell A C and Segur H 1974 Stud. Appl. Math. 53 249
[34] Miura R M 1974 Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications (Berlin:Springer)
[35] Hirota R and Satsuma J 1981 Phys. Lett. A 85 407
[36] Hietarinta J 2004 Integrability of Nonlinear Systems 638 95
[37] Zhou Y, Manukure S and Ma W X 2019 Commun. Nonlinear Sci. Numer. Simul. 68 56
[38] Yan X Y, Liu J Z and Xin X P 2023 Chin. Phys. B 32 070201
[39] Ma W X 2011 Stud. Nonlinear Sci. 2 140
[40] Zhang X E and Chen Y 2017 Commun. Nonlinear Sci. Numer. Simul. 52 24
[41] Wang S, Tang X and Lou S Y 2004 Chaos, Solitons and Fractals 21 231
[42] Or-Roshid H and Rashidi M M 2017 J. Ocean Eng. Sci. 2 120

Localized wave solutions and interactions of the (2+1)-dimensional Hirota—Satsuma—Ito equation

Localized wave solutions and interactions of the (2+1)-dimensional Hirota—Satsuma—Ito 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 7

Metrics

本文评价

推荐阅读 0

[1]	Hongcai Ma(马红彩), Xue Mao(毛雪), and Aiping Deng(邓爱平). Interaction solutions for the second extended (3+1)-dimensional Jimbo-Miwa equation[J]. 中国物理B, 2023, 32(6): 60201-060201.
[2]	Feng Yuan(袁丰), Behzad Ghanbari, Yongshuai Zhang(张永帅), and Abdul Majid Wazwaz. From breather solutions to lump solutions: A construction method for the Zakharov equation[J]. 中国物理B, 2023, 32(12): 120201-120201.
[3]	Jun-Cai Pu(蒲俊才), Jun Li(李军), and Yong Chen(陈勇). Soliton, breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints[J]. 中国物理B, 2021, 30(6): 60202-060202.
[4]	王海峰, 张玉峰. Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation[J]. 中国物理B, 2020, 29(4): 40501-040501.
[5]	刘健, 吴剑文. Lump and interaction solutions to the (3+1)-dimensional Burgers equation[J]. 中国物理B, 2020, 29(3): 30201-030201.
[6]	郑攀峰, 贾曼. A more general form of lump solution, lumpoff, and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation[J]. 中国物理B, 2018, 27(12): 120201-120201.
[7]	宋彩芹, 肖冬梅, 朱佐农. Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation[J]. 中国物理B, 2017, 26(10): 100204-100204.