Interactions between Solitons and Cnoidal Periodic Waves of the Gardner Equation

doi:10.1088/0256-307X/31/7/070203

Chin. Phys. Lett.

2014, Vol. 31

Issue (07): 070203 DOI: 10.1088/0256-307X/31/7/070203

GENERAL

Interactions between Solitons and Cnoidal Periodic Waves of the Gardner Equation

YU Wei-Feng^1,2**, LOU Sen-Yue^1,3, YU Jun², HU Han-Wei⁴

¹Faculty of Science, Ningbo University, Ningbo 315211
²Department of Physics, Shaoxing University, Shaoxing 312000
³Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062
⁴Department of Physics, Beilun Minggang High School, Ningbo 315211

Cite this article:

YU Wei-Feng, LOU Sen-Yue, YU Jun et al 2014 Chin. Phys. Lett. 31 070203

Download: PDF(539KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract The Gardner equation is one of the most important prototypic models in nonlinear physics. Many scholars pay much attention to the Gardner equation and various nonlinear excitations of the Gardner equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this work, with the help of the Riccati equation, the Gardner equation is solved by the consistent Riccati expansion. Furthermore, we obtain the soliton-cnoidal wave interaction solutions of the Gardner equation.

Published: 30 June 2014

PACS:	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)

TRENDMD:

URL:

https://cpl.iphy.ac.cn/10.1088/0256-307X/31/7/070203 OR https://cpl.iphy.ac.cn/Y2014/V31/I07/070203

Service
	E-mail this article
	E-mail Alert
	RSS
Articles by authors
	YU Wei-Feng
	LOU Sen-Yue
	YU Jun
	HU Han-Wei

[1] Wadati M 1975 J. Phys. Soc. Jpn. 38 673
[2] Knonno K 1974 J. Phys. Soc. Jpn. 37 1631
[3] Tappert F D 1970 Phys. Rev. Lett. 25 1108
[4] Narayanamurti V 1970 Phys. Rev. Lett. 25 1105
[5] Coffey M W 1990 SIAM J. Appl. Math. 50 1580
[6] Wadati M 1975 J. Phys. Soc. Jpn. 38 681
[7] Mohamad M N 1992 Energy Sources 14 73
[8] Lou S Y 2013 arXiv:1308.5891[nlin.SI]
[9] Liu S K, Fu Z T, Liu S D and Zhao Q 2002 Acta Phys. Sin. 51 10 (in Chinese)

Related articles from Frontiers Journals

[1]	S. Y. Lou, Man Jia, and Xia-Zhi Hao. Higher Dimensional Camassa–Holm Equations[J]. Chin. Phys. Lett., 2023, 40(2): 070203
[2]	Wen-Xiu Ma. Matrix Integrable Fourth-Order Nonlinear Schr?dinger Equations and Their Exact Soliton Solutions[J]. Chin. Phys. Lett., 2022, 39(10): 070203
[3]	Chong Liu, Shao-Chun Chen, Xiankun Yao, and Nail Akhmediev. Modulation Instability and Non-Degenerate Akhmediev Breathers of Manakov Equations[J]. Chin. Phys. Lett., 2022, 39(9): 070203
[4]	Xiao-Man Zhang, Yan-Hong Qin, Li-Ming Ling, and Li-Chen Zhao. Inelastic Interaction of Double-Valley Dark Solitons for the Hirota Equation[J]. Chin. Phys. Lett., 2021, 38(9): 070203
[5]	Kai-Hua Yin, Xue-Ping Cheng, and Ji Lin. Soliton Molecule and Breather-Soliton Molecule Structures for a General Sixth-Order Nonlinear Equation[J]. Chin. Phys. Lett., 2021, 38(8): 070203
[6]	Yusong Cao and Junpeng Cao. Exact Solution of a Non-Hermitian Generalized Rabi Model[J]. Chin. Phys. Lett., 2021, 38(8): 070203
[7]	Zequn Qi , Zhao Zhang , and Biao Li. Space-Curved Resonant Line Solitons in a Generalized $(2+1)$-Dimensional Fifth-Order KdV System[J]. Chin. Phys. Lett., 2021, 38(6): 070203
[8]	Wei Wang, Ruoxia Yao, and Senyue Lou. Abundant Traveling Wave Structures of (1+1)-Dimensional Sawada–Kotera Equation: Few Cycle Solitons and Soliton Molecules[J]. Chin. Phys. Lett., 2020, 37(10): 070203
[9]	Li-Chen Zhao, Yan-Hong Qin, Wen-Long Wang, Zhan-Ying Yang. A Direct Derivation of the Dark Soliton Excitation Energy[J]. Chin. Phys. Lett., 2020, 37(5): 070203
[10]	Danda Zhang, Da-Jun Zhang, Sen-Yue Lou. Lax Pairs of Integrable Systems in Bidifferential Graded Algebras[J]. Chin. Phys. Lett., 2020, 37(4): 070203
[11]	Yu-Han Wu, Chong Liu, Zhan-Ying Yang, Wen-Li Yang. Breather Interaction Properties Induced by Self-Steepening and Space-Time Correction[J]. Chin. Phys. Lett., 2020, 37(4): 070203
[12]	Bao Wang, Zhao Zhang, Biao Li. Soliton Molecules and Some Hybrid Solutions for the Nonlinear Schr?dinger Equation[J]. Chin. Phys. Lett., 2020, 37(3): 070203
[13]	Zhao Zhang, Shu-Xin Yang, Biao Li. Soliton Molecules, Asymmetric Solitons and Hybrid Solutions for (2+1)-Dimensional Fifth-Order KdV Equation[J]. Chin. Phys. Lett., 2019, 36(12): 070203
[14]	Zhou-Zheng Kang, Tie-Cheng Xia. Construction of Multi-soliton Solutions of the $N$-Coupled Hirota Equations in an Optical Fiber[J]. Chin. Phys. Lett., 2019, 36(11): 070203
[15]	Yong-Shuai Zhang, Jing-Song He. Bound-State Soliton Solutions of the Nonlinear Schr?dinger Equation and Their Asymmetric Decompositions[J]. Chin. Phys. Lett., 2019, 36(3): 070203

Viewed

Full text

Abstract