Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation

doi:10.1088/1674-1056/ac89d9

中国物理B ›› 2023, Vol. 32 ›› Issue (3): 30505-030505.doi: 10.1088/1674-1056/ac89d9

Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation

Yiyuan Zhang(张艺源), Ziqi Liu(刘子琪), Jiaxin Qi(齐家馨), and Hongli An(安红利)^†

College of Sciences, Nanjing Agricultural University, Nanjing 210000, China

收稿日期:2022-07-07 修回日期:2022-08-08 接受日期:2022-08-16 出版日期:2023-02-14 发布日期:2023-03-03
通讯作者: Hongli An E-mail:kaixinguoan@163.com
基金资助:
Project supported by Jiangsu Provincial Natural Science Foundation of China (Grant Nos. BK20221508, 11775116, BK20210380, and JSSCBS20210277), SRT (Grant No. 202210307165Y), and Jiangsu Qinglan High-level Talent Project.

Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation

Yiyuan Zhang(张艺源), Ziqi Liu(刘子琪), Jiaxin Qi(齐家馨), and Hongli An(安红利)^†

College of Sciences, Nanjing Agricultural University, Nanjing 210000, China

Received:2022-07-07 Revised:2022-08-08 Accepted:2022-08-16 Online:2023-02-14 Published:2023-03-03
Contact: Hongli An E-mail:kaixinguoan@163.com
Supported by:
Project supported by Jiangsu Provincial Natural Science Foundation of China (Grant Nos. BK20221508, 11775116, BK20210380, and JSSCBS20210277), SRT (Grant No. 202210307165Y), and Jiangsu Qinglan High-level Talent Project.

摘要/Abstract

摘要： By employing the complexification method and velocity resonant principle to $N$-solitons of the $(2+1)$-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (KDKK) equation, we obtain the soliton molecules, $T$-breather molecules, $T$-breather-$L$-soliton molecules and some interaction solutions when $N\leq6$. Dynamical behaviors of these solutions are discussed analytically and graphically. The method adopted can be effectively used to construct soliton molecules and $T$-breather molecules of other nonlinear evolution equations. The results obtained may be helpful for experts to study the related phenomenon in oceanography and atmospheric science.

关键词: soliton molecules, breather molecules, interaction solutions, velocity resonant principle, Konopelchenko-Dubrovsky-Kaup-Kupershmidt (KDKK) equation

Abstract: By employing the complexification method and velocity resonant principle to $N$-solitons of the $(2+1)$-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (KDKK) equation, we obtain the soliton molecules, $T$-breather molecules, $T$-breather-$L$-soliton molecules and some interaction solutions when $N\leq6$. Dynamical behaviors of these solutions are discussed analytically and graphically. The method adopted can be effectively used to construct soliton molecules and $T$-breather molecules of other nonlinear evolution equations. The results obtained may be helpful for experts to study the related phenomenon in oceanography and atmospheric science.

Key words: soliton molecules, breather molecules, interaction solutions, velocity resonant principle, Konopelchenko-Dubrovsky-Kaup-Kupershmidt (KDKK) equation

中图分类号: (Solitons)

05.45.Yv

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

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.

参考文献

[1] Whitham G B 1974 Linear and Nonlinear Waves (New York: John Wiley & Sons) p. 120
[2] Kundu P K 1990 Fluid Mechanics (San Diego: Academic Press) p. 155
[3] Lamb H 1945 Hydrodynamics (New York: Cambridge University Press) p. 1932
[4] Yang X Y, Fan R and Li B 2020 Phys. Scripta 95 045213
[5] Peng W Q, Tian S F and Zhang T T 2018 Phys. Lett. A 382 2701
[6] Wang H, Tian S F, Zhang T T and Chen Y 2019 Front. Math. China 14 631
[7] Lan Z Z, Gao Y T, Yang J W, Su C Q and Wang Q M 2016 Mod. Phys. Lett. B 30 1650265
[8] Yang T Y and Ma W X 2016 Int. J. Mod. Phys. B 30 1640028
[9] Lü X and Li J 2014 Nonlinear Dyn. 77 135
[10] Xin X P, Liu X Q and Zhang L L 2010 Appl. Math. Comput. 215 3669
[11] Sawada K and Kotera T 1974 Prog. Theor. Phys. 51 1355
[12] Konopelehenko B and Dubrovsky V 1984 Phys. Lett. A 102 15
[13] Zhang H Q and Ma W X 2017 Nonlinear Dyn. 87 2305
[14] Li X, Wang Y, Chen M D and Li B 2017 Adv. Math. Phys. 2017 1743789
[15] An H L, Feng D L and Zhu H X 2019 Nonlinear Dyn. 98 1275
[16] Feng L L, Tian S F, Yan H, Wang L and Zhang T T 2016 Eur. Phys. J. Plus. 131 241
[17] Liu W H, Zhang Y F and Shi D D 2019 Commun. Theor. Phys. 71 670
[18] Deng G F, Gao Y T, Ding C C and Su J J 2020 Chaos Soliton. Fract. 140 110085
[19] Yuan P S, Qi J X, Li Z L and An H L 2020 Chin. Phys. B 30 040503
[20] Zhang C Y, Gao Y T, Li L Q and Ding C C 2020 Nonlinear Dyn. 102 1773
[21] Ma H C, Cheng Q X and Deng A P 2020 Commun. Theor. Phys. 72 095001
[22] Barashenkov I V, Smirnov Y S and Alexeeva N V 1998 Phys. Rev. E 57 2350
[23] Barashenkov I V and Zemlyanaya E V 1999 Phys. Rev. Lett. 83 2568
[24] Akhmediev N and Ankiewicz A 2000 Chaos 10 600
[25] Stratmann M, Pagel T and Mitschke F 2005 Phys. Rev. Lett. 95 143902
[26] Weng W, Bouchand R, Lucas E, Obrzud E, Herr T and Kippenberg T 2019 Nat. Commun. 11 2402
[27] Rohrmann P, Hause A and Mitschke F 2012 Sci. Rep. 2 866
[28] Herink G, Kurtz F, Jalali B, Solli D and Ropers C 2017 Science 356 50
[29] Liu X M, Yao X K and Cui Y D 2018 Phys. Rev. Lett. 121 023905
[30] Wang C, Wang L, Li X H, et al. 2019 Nanotechnology 30 025204
[31] Wang Z Q, Nithyanandan K, Coillet A, Tchofo-Dinda P and Grelu P 2019 Nat. Commun. 10 830
[32] Lakomy K, Nath R and Santos L 2012 Phys. Rev. A 86 013610
[33] Kivshar Y S and Malomed B A 1989 Rev. Mod. Phys. 61 763
[34] Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240
[35] Crasovan L C, Kartashov Y V, Mihalache D, Torner L and Kivshar Y S 2003 Phys. Rev. E 67 046610
[36] Yin C Y and Berloff N G 2011 Phys. Rev. A 83 051605
[37] Lou S Y 2020 J. Phys. Commun. 4 041002
[38] Yan Z W and Lou S Y 2020 Appl. Math. Lett. 104 106271
[39] Yan Z and Lou S Y 2020 Commun. Nonlinear Sci. Numer. Simul. 91 105425
[40] Zhang Z, Yang X Y and Li B 2020 Appl. Math. Lett. 103 106168
[41] Cui C J, Tang X Y and Cui Y J 2020 Appl. Math. Lett. 102 106109
[42] Zhang Z, Yang X Y and Li B 2020 Nonlinear Dyn. 100 1551
[43] Zhang Z, Yang S X and Li B 2019 Chin. Phys. Lett. 36 120501
[44] Dong J J, Li B and Yuen M W 2020 Commun. Theor. Phys. 72 075501
[45] Hirota R 2004 The Direct Method in Soliton Theory (NewYork: Cambridge University Press)
[46] Ablowitza M J and Satsuma J 1978 J. Math. Phys. 19 2180
[47] Satsuma J and Ablowitz M J 1979 J. Math. Phys. 20 1496

Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation

Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK 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 5

Metrics

本文评价

推荐阅读 0

[1]	Zhonglong Zhao(赵忠龙), Lingchao He(和玲超), and Abdul-Majid Wazwaz. Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves[J]. 中国物理B, 2023, 32(4): 40501-040501.
[2]	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.
[3]	Hongcai Ma(马红彩), Yuxin Wang(王玉鑫), and Aiping Deng(邓爱平). Soliton molecules and asymmetric solitons of the extended Lax equation via velocity resonance[J]. 中国物理B, 2022, 31(1): 10201-010201.
[4]	楼森岳. A novel (2+1)-dimensional integrable KdV equation with peculiar solution structures[J]. 中国物理B, 2020, 29(8): 80502-080502.
[5]	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.