Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation

doi:10.1088/1674-1056/ab75d7

中国物理B ›› 2020, Vol. 29 ›› Issue (4): 40501-040501.doi: 10.1088/1674-1056/ab75d7

Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation

Haifeng Wang(王海峰), Yufeng Zhang(张玉峰)

School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China

收稿日期:2020-01-02 修回日期:2020-01-28 出版日期:2020-04-05 发布日期:2020-04-05
通讯作者: Yufeng Zhang E-mail:zhangyfcumt@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11971475).

Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation

Haifeng Wang(王海峰), Yufeng Zhang(张玉峰)

School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China

Received:2020-01-02 Revised:2020-01-28 Online:2020-04-05 Published:2020-04-05
Contact: Yufeng Zhang E-mail:zhangyfcumt@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11971475).

摘要/Abstract

摘要： We study a simplified (3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method. Then, a more general form of lump solution is constructed, which contains more arbitrary autocephalous parameters. In addition, a lumpoff solution is also derived based on the general lump solutions and a stripe soliton. Furthermore, we figure out instanton/rogue wave solutions via introducing two stripe solitons. Finally, one can better illustrate these propagation phenomena of these solutions by analyzing images.

关键词: dimensionally reduced Hirota bilinear equation, more general form of lump solution, lumpoff solution, rogue wave solution

Abstract: We study a simplified (3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method. Then, a more general form of lump solution is constructed, which contains more arbitrary autocephalous parameters. In addition, a lumpoff solution is also derived based on the general lump solutions and a stripe soliton. Furthermore, we figure out instanton/rogue wave solutions via introducing two stripe solitons. Finally, one can better illustrate these propagation phenomena of these solutions by analyzing images.

Key words: dimensionally reduced Hirota bilinear equation, more general form of lump solution, lumpoff solution, rogue wave solution

中图分类号: (Solitons)

05.45.Yv

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

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.

Haifeng Wang(王海峰), Yufeng Zhang(张玉峰). Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation[J]. Chin. Phys. B, 2020, 29(4): 40501-040501.

[1]	Solli D R, Ropers C, Koonath P and Jalali B 2007 Nature 450 1054 doi: 10.1038/nature06402
[2]	Müller P, Garrett C and Osborne A 2005 Oceanography 18 66 doi: 10.5670/oceanog.2005.30
[3]	Ma W X 2015 Phys. Lett. A 379 1975 doi: 10.1016/j.physleta.2015.06.061
[4]	Ma W X and Zhou Y 2018 J. Differ. Equ. 264 2633 doi: 10.1016/j.jde.2017.10.033
[5]	Lü X, Chen S T and Ma W X 2016 Nonlinear Dyn. 86 523 doi: 10.1007/s11071-016-2905-z
[6]	Yang J Y and Ma W X 2016 Int. J. Mod. Phys. B 30 1640028 doi: 10.1142/S0217979216400282
[7]	Yang J Y, Ma W X and Qin Z Y 2018 Anal. Math. Phys. 8 427 doi: 10.1007/s13324-017-0181-9
[8]	Wang H 2018 Appl. Math. Lett. 85 27 doi: 10.1016/j.aml.2018.05.010
[9]	Lü X, Tian B and Qi F H 2012 Nonlinear Anal-Real 13 1130 doi: 10.1016/j.nonrwa.2011.09.006
[10]	Manakov S V, Zakharov V E, Bordag L A, Its A R and Matveev V B 1977 Phys. Lett. A 63 205 doi: 10.1016/0375-9601(77)90875-1
[11]	Ma W X 2018 J. Geom. Phys. 133 10 doi: 10.1016/j.geomphys.2018.07.003
[12]	Ma W X, Yong X and Zhang H Q 2018 Comput. Math. Appl. 75 289 doi: 10.1016/j.camwa.2017.09.013
[13]	Ma W X 2013 Rep. Math. Phys. 72 41 doi: 10.1016/S0034-4877(14)60003-3
[14]	Ma W X 2019 Mod. Phys. Lett. B 33 1950457 doi: 10.1142/S0217984919504578
[15]	Ma W X 2019 J. Appl. Anal. Comput. 9 1319
[16]	Ma W X 2019 Front. Math. Chin. 14 619 doi: 10.1007/s11464-019-0771-y
[17]	Wang H F and Zhang Y F 2019 Symmetry 11 1365 doi: 10.3390/sym11111365
[18]	Zhang Y, Liu Y P and Tang X Y 2018 Comput. Math. Appl. 76 592 doi: 10.1016/j.camwa.2018.04.039
[19]	Zhang Y F and Ma W X 2015 Z. Naturforsch. A 70 263 doi: 10.1515/zna-2014-0361
[20]	Tang X Y, Lou S Y and Zhang Y 2002 Phys. Rev. E 66 046601 doi: 10.1103/PhysRevE.66.046601
[21]	Yang J Y and Ma W X 2017 Nonlinear Dyn. 89 1539 doi: 10.1007/s11071-017-3533-y
[22]	Shats M, Punzmann H and Xia H 2010 Phys. Rev. Lett. 104 104503 doi: 10.1103/PhysRevLett.104.104503
[23]	Ginzburg N S, Rozental R M, Sergeev A S, Fedotov A E, Zotova I V and Tarakanov V P 2017 Phys. Rev. Lett. 119 034801 doi: 10.1103/PhysRevLett.119.034801
[24]	Moslem W M, Shukla P K and Eliasson B 2011 Europhys. Lett. 96 25002 doi: 10.1209/0295-5075/96/25002
[25]	Höhmann R, Kuhl U, Stöckmann H J, Kaplan L and Heller E J 2010 Phys. Rev. Lett. 104 093901 doi: 10.1103/PhysRevLett.104.093901
[26]	Satsuma J and Ablowitz M J 1979 J. Math. Phys. 20 1496 doi: 10.1063/1.524208
[27]	Osman M S and Machado J A T 2018 Nonlinear Dyn. 93 733 doi: 10.1007/s11071-018-4222-1
[28]	Sun Y, Tian B, Xie X Y, Chai J and Yin H M 2018 Wave. Random Complex 28 544 doi: 10.1080/17455030.2017.1367866
[29]	Villarroel J, Prada J and Estévez P G 2009 Stud. Appl. Math. 122 395 doi: 10.1111/j.1467-9590.2009.00440.x
[30]	Liu J G, Yang X J, Cheng M H, Fenf Y Y and Wang Y D 2019 Comput. Math. Appl. 78 1947 doi: 10.1016/j.camwa.2019.03.034
[31]	Akhmediev N, Ankiewicz A and Taki M 2009 Phys. Lett. A 373 675 doi: 10.1016/j.physleta.2008.12.036
[32]	Jia M and Lou S Y 2018 arXiv:1803.01730v1[nlin.SI]
[33]	Wu P X and Zhang Y F 2019 Phys. Lett. A 383 1755 doi: 10.1016/j.physleta.2019.03.005
[34]	Mao J J, Tian S F, Zou L, Zhang T T and Yan X J 2019 Nonlinear Dyn. 95 3005 doi: 10.1007/s11071-018-04736-2
[35]	Peng W Q, Tian S F and Zhang T T 2018 Phys. Lett. A 382 2701 doi: 10.1016/j.physleta.2018.08.002
[36]	Zheng P F and Jia M 2018 Chin. Phys. B 27 120201 doi: 10.1088/1674-1056/27/12/120201
[37]	Gao L N, Zhao X Y, Zi Y Y, Yu J and Lü X 2016 Comput. Math. Appl. 72 1225 doi: 10.1016/j.camwa.2016.06.008
[38]	Lü X and Ma W X 2016 Nonlinear Dyn. 85 1217 doi: 10.1007/s11071-016-2755-8
[39]	Hirota R 1971 Phys. Rev. Lett. 27 1192 doi: 10.1103/PhysRevLett.27.1192
[40]	Hirota R 2004 Direct Method Soliton Theory (Cambridge: Cambridge University Press) p. 155

[1]	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.
[2]	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.
[3]	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.

Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation

Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 40

相关文章 3

Metrics

本文评价

推荐阅读 0