Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev–Petviashvili equation

doi:10.1088/1674-1056/20/1/015205

Abstract In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions.

Keywords: Kadomtsev–Petviashvili equation soliton resonance

Received: 04 June 2010
Revised: 22 July 2010
Accepted manuscript online:

PACS:	52.35.Sb	(Solitons; BGK modes)
	05.45.Yv	(Solitons)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10575082); the Key Project Foundation of the Education Ministry of China (Grant No. 209128), the Natural Science Foundation of Northwest Normal University (Grant No. NWNU-KJCXGC-03-53).

Cite this article:

Shi Yu-Ren(石玉仁), Zhang Juan(张娟), Yang Hong-Juan(杨红娟), Duan Wen-Shan(段文山), and Karl E. Lonngren Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev–Petviashvili equation 2011 Chin. Phys. B 20 015205

[1]	Kadomtesv B B and Petviashvili V I 1970 Sov. Phys. Doklady. 15 539
[2]	Tsikis E K, Raychaudhuri S, Gabl E F and Lonngren K E 1985 Plasma Phys. Controlled Fusion 27 419
[3]	Miles J W 1977 J. Fluid Mech. 79 171
[4]	Maxworthy T 1980 J. Fluid. Mech. 96 47
[5]	Duan W S, Shi Y R and Hong X R 2004 Phys. Lett. A 323 89
[6]	Yang H J, Shi Y R and Duan W S 2006 Front. Phys. China 4 1
[7]	Lonngren K E 1998 Opt. Quantum. Electron. 30 615
[8]	Nakamura Y, Bailung H and Lonngren K E 1999 Phys. Plasmas 6 3466
[9]	Tsukabayashi I and Nakamura Y 1981 Phys. Lett. A 85 151
[10]	Tsukabayashi I, Nakamura Y, Kako F and Lonngren K E 1983 Phys. Fluid 26 790
[11]	Nakamura Y, Bailung H and Lonngren K E 1999 J. Plasma. Phys. 6 3466
[12]	Ze F, Hershkowitz N, Chen C and Lonngren K E 1979 Phys. Rev. Lett. 42 1747
[13]	Lin M M and Duan W S 2004 Phys. Plasmas 11 5710
[14]	Lin M M and Duan W S 2005 Chaos, Solitons and Fractals 23 929
[15]	Shi Y R, Guo P, L"u K P and Duan W S 2004 Acta Phys. Sin. 53 3265 (in Chinese)
[16]	Shi Y R, L"u K P, Duan W S, Hong X R, Zhao J B and Yang H J 2003 Acta Phys. Sin. 52 267 (in Chinese)
[17]	Duan W S, Wan G X, Wang X Y and Lin M M 2004 Phys. Plasmas 11 4408
[18]	Duan W S 2003 Phys. Lett. A 317 275
[19]	Duan W S and Shi Y R 2003 Chaos, Solitons and Fractals 18 321
[20]	Hirota R 1971 Phys. Rev. Lett. 27 1192
[21]	Ruan H Y and Chen Y X 2000 Phys. Rev. E 62 5738
[22]	Ruan H Y and Chen Y X 1999 J. Math. Phys. 40 248
[23]	Ruan H Y 1999 Acta Phys. Sin. 48 1781 (in Chinese)
[24]	Ruan H Y 2001 Acta Phys. Sin. 50 329 (in Chinese)
[25]	Ruan H Y and Chen Y X 2003 Acta Phys. Sin. 52 1313 (in Chinese)
[26]	Ruan H Y 2004 Acta Phys. Sin. 53 1617 (in Chinese)
[27]	Yan Z Y and Zhang H Q 2001 Phys. Lett. A 285 355
[28]	Ying J P and Lou S Y 2003 Chin. Phys. Lett. 20 1448
[29]	Fang J P, Zheng C L and Zhu J M 2005 Commun. Theor. Phys. 44 203
[30]	Fang J P and Zheng C L 2005 Chin. Phys. 14 670
[31]	Zhang S L, Lou S Y and Qu C Z 2006 Chin. Phys. 15 2765
[32]	Ma H C, Ge D J and Yu Y D 2008 Chin. Phys. B 17 1448
[33]	Adler M and Moser J 1978 Comm. Math. Phys. 61 1
[34]	Ehlers F and Knorrer H 1982 Comment. Math. Helv. 57 1
[35]	Svinolupov S I, Sokolov V and Yamilov R 1983 Soviet. Math. Dokl. 28 165
[36]	Hirose A and Lonngren K E 2010 Fundamentals of Wave Phenomena (Raleigh: SciTech Publishing Inc), Chapter 15 endfootnotesize

[1]	Riemann--Hilbert approach of the complex Sharma—Tasso—Olver equation and its N-soliton solutions Sha Li(李莎), Tiecheng Xia(夏铁成), and Hanyu Wei(魏含玉). Chin. Phys. B, 2023, 32(4): 040203.
[2]	Precision measurement and suppression of low-frequency noise in a current source with double-resonance alignment magnetometers Jintao Zheng(郑锦韬), Yang Zhang(张洋), Zaiyang Yu(鱼在洋), Zhiqiang Xiong(熊志强), Hui Luo(罗晖), and Zhiguo Wang(汪之国). Chin. Phys. B, 2023, 32(4): 040601.
[3]	Resonant perfect absorption of molybdenum disulfide beyond the bandgap Hao Yu(于昊), Ying Xie(谢颖), Jiahui Wei(魏佳辉), Peiqing Zhang(张培晴),Zhiying Cui(崔志英), and Haohai Yu(于浩海). Chin. Phys. B, 2023, 32(4): 048101.
[4]	Application of the body of revolution finite-element method in a re-entrant cavity for fast and accurate dielectric parameter measurements Tianqi Feng(冯天琦), Chengyong Yu(余承勇), En Li(李恩), and Yu Shi(石玉). Chin. Phys. B, 2023, 32(3): 030101.
[5]	All-optical switches based on three-soliton inelastic interaction and its application in optical communication systems Shubin Wang(王树斌), Xin Zhang(张鑫), Guoli Ma(马国利), and Daiyin Zhu(朱岱寅). Chin. Phys. B, 2023, 32(3): 030506.
[6]	Numerical simulation of a truncated cladding negative curvature fiber sensor based on the surface plasmon resonance effect Zhichao Zhang(张志超), Jinhui Yuan(苑金辉), Shi Qiu(邱石), Guiyao Zhou(周桂耀), Xian Zhou(周娴), Binbin Yan(颜玢玢), Qiang Wu(吴强), Kuiru Wang(王葵如), and Xinzhu Sang(桑新柱). Chin. Phys. B, 2023, 32(3): 034208.
[7]	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). Chin. Phys. B, 2023, 32(3): 030505.
[8]	Inverse stochastic resonance in modular neural network with synaptic plasticity Yong-Tao Yu(于永涛) and Xiao-Li Yang(杨晓丽). Chin. Phys. B, 2023, 32(3): 030201.
[9]	Fiber cladding dual channel surface plasmon resonance sensor based on S-type fiber Yong Wei(魏勇), Xiaoling Zhao(赵晓玲), Chunlan Liu(刘春兰), Rui Wang(王锐), Tianci Jiang(蒋天赐), Lingling Li(李玲玲), Chen Shi(石晨), Chunbiao Liu(刘纯彪), and Dong Zhu(竺栋). Chin. Phys. B, 2023, 32(3): 030702.
[10]	Electrical manipulation of a hole ‘spin’-orbit qubit in nanowire quantum dot: The nontrivial magnetic field effects Rui Li(李睿) and Hang Zhang(张航). Chin. Phys. B, 2023, 32(3): 030308.
[11]	Real-time observation of soliton pulsation in net normal-dispersion dissipative soliton fiber laser Xu-De Wang(汪徐德), Xu Geng(耿旭), Jie-Yu Pan(潘婕妤), Meng-Qiu Sun(孙梦秋), Meng-Xiang Lu(陆梦想), Kai-Xin Li(李凯芯), and Su-Wen Li(李素文). Chin. Phys. B, 2023, 32(2): 024210.
[12]	Matrix integrable fifth-order mKdV equations and their soliton solutions Wen-Xiu Ma(马文秀). Chin. Phys. B, 2023, 32(2): 020201.
[13]	Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system Huamei Yang(杨华美) and Yuangen Yao(姚元根). Chin. Phys. B, 2023, 32(2): 020501.
[14]	A cladding-pumping based power-scaled noise-like and dissipative soliton pulse fiber laser Zhiguo Lv(吕志国), Hao Teng(滕浩), and Zhiyi Wei(魏志义). Chin. Phys. B, 2023, 32(2): 024207.
[15]	Dual-channel fiber-optic surface plasmon resonance sensor with cascaded coaxial dual-waveguide D-type structure and microsphere structure Ling-Ling Li(李玲玲), Yong Wei(魏勇), Chun-Lan Liu(刘春兰), Zhuo Ren(任卓), Ai Zhou(周爱), Zhi-Hai Liu(刘志海), and Yu Zhang(张羽). Chin. Phys. B, 2023, 32(2): 020702.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev–Petviashvili equation

Cite this article:

Online attention