B?cklund Transformations and Interaction Solutions of the Burgers Equation

doi:10.1088/0256-307X/30/2/020203

Chin. Phys. Lett.

2013, Vol. 30

Issue (2): 020203 DOI: 10.1088/0256-307X/30/2/020203

GENERAL

B?cklund Transformations and Interaction Solutions of the Burgers Equation

JIN Yan¹, JIA Man², LOU Sen-Yue^2,3**

¹Ningbo Institute of Education, Ningbo 315010
²Faculty of Science, Ningbo University, Ningbo 315211
³Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062

Cite this article:

JIN Yan, JIA Man, LOU Sen-Yue 2013 Chin. Phys. Lett. 30 020203

Download: PDF(483KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract The Burgers equation is one of the most important prototypic models in nonlinear physics. Various exact solutions of the Burgers equation have been found by many methods. However, it is very difficult to find interactive solutions among different types of nonlinear excitations. We develop a generalized tanh function expansion approach, which can be considered as the B?cklund transformation, to find interactive solutions between the soliton and other types of Burgers waves.

Received: 30 August 2012 Published: 02 March 2013

PACS:	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)
	47.35.Fg	(Solitary waves)
	52.35.Sb	(Solitons; BGK modes)
	47.35.Lf	(Wave-structure interactions)

TRENDMD:

URL:

https://cpl.iphy.ac.cn/10.1088/0256-307X/30/2/020203 OR https://cpl.iphy.ac.cn/Y2013/V30/I2/020203

Service
	E-mail this article
	E-mail Alert
	RSS
Articles by authors
	JIN Yan
	JIA Man
	LOU Sen-Yue

[1] Kivshar Yu S and Malomed B A 1989 Rev. Mod. Phys. 61 763
Kivshar Yu S and Luther-Davies B 1998 Phys. Rep. 298 81
[2] Pudasaini S P 2011 Phys. Fluids 23 043301
[3] Lou S Y and Lian Z J 2005 Chin. Phys. Lett. 22 1
[4] Olver P J 1993 Application of Lie Groups to Differential Equation, Graduate Texts in Mathematics 2nd edn (New York: Springer-Verlag)
[5] Lou S Y and Hu X B 1993 Chin. Phys. Lett. 10 577
Lou S Y and Hu X B 1997 J. Math. Phys. 38 6401
Lou S Y and Hu X B 1997 J. Phys. A 30 L95
[6] G Bluman, A Cheviakov and S Anco 2010 Appl. Math. Sci. vol 168 Symmetry Methods Partial Differential Equations (New York: Springer)
[7] Lou S Y 1993 Phys. Lett. B 302 261
Lou S Y 1994 J. Math. Phys. 35 2390
[8] Lou S Y 1998 Phys. Scr. 57 481
Hu X B, Lou S Y and Qian X M 2009 Stud. Appl. Math. 122 305
[9] Lou S Y 1997 J. Phys. A: Math. Phys. 30 4803
[10] Hu X R, Lou S Y and Chen Y 2012 Phys. Rev. E 85 056607
Gu C H, Hu H S and Zhou Z X 2005 Darboux Transformations Integrable Systems Theory Their Appl. Geometry Ser.: Math. Phys. Studies vol 26 (Berlin: Springer)
[11] Lou S Y, Hu X R and Chen Y 2012 J. Phys. A: Math. Theor. 45 155209
Rogers C and Schief W K 2002 B?cklund and Darboux Transformations Geometry and Modern Applications in Soliton Theory, Cambridgetexts in Applied Mathematics (Cambridge: Cambridge University Press)
[12] Cheng X P, Chen C L and Lou S Y 2012 Interactions among Different Types of Nonlinear Waves Described by the Kadomtsev–Petviashvili Equation arXiv:1208.3259
[13] Lan H B and Wang K L 1990 J. Phys. A 23 3923
Chen W Z and Lou S Y 1991 Commun. Theor. Phys. 16 89
[14] Lou S Y and Ni G J 1990 Sing. J. Phys. 7 47
Huang G X, Lou S Y and Dai X X 1989 Phys. Lett. A 139 373
Fan E G 2000 Phys. Lett. A 277 212

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): 020203
[2]	Wen-Xiu Ma. Matrix Integrable Fourth-Order Nonlinear Schr?dinger Equations and Their Exact Soliton Solutions[J]. Chin. Phys. Lett., 2022, 39(10): 020203
[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): 020203
[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): 020203
[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): 020203
[6]	Yusong Cao and Junpeng Cao. Exact Solution of a Non-Hermitian Generalized Rabi Model[J]. Chin. Phys. Lett., 2021, 38(8): 020203
[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): 020203
[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): 020203
[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): 020203
[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): 020203
[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): 020203
[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): 020203
[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): 020203
[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): 020203
[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): 020203

Viewed

Full text

Abstract