Conservation laws of the generalized short pulse equation

doi:10.1088/1674-1056/24/2/020201

Abstract We show that the generalized short pulse equation is nonlinearly self-adjoint with differential substitution. Moreover, any adjoint symmetry is a differential substitution of nonlinear self-adjointness, and vice versa. Consequently, the general conservation law formula is constructed and new conservation laws for some special cases are found.

Keywords: nonlinear self-adjointness with differential substitution adjoint symmetry conservation law

Received: 20 July 2014
Revised: 02 September 2014
Accepted manuscript online:

PACS:	02.20.Sv	(Lie algebras of Lie groups)
	02.30.Jr	(Partial differential equations)
	11.30.-j	(Symmetry and conservation laws)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11301012 and 11271363), the Excellent Young Teachers Program of North China University of Technology (Grant No. 14058) and the Doctoral Fund of North China University of Technology (Grant No. 41).

Corresponding Authors: Zhang Zhi-Yong
E-mail: zhiyong-2008@163.com

Cite this article:

Zhang Zhi-Yong (张智勇), Chen Yu-Fu (陈玉福) Conservation laws of the generalized short pulse equation 2015 Chin. Phys. B 24 020201

[1]	Schäfer T and Wayne C E 2004 Physica D 196 90
[2]	Brunelli J C 2006 Phys. Lett. A 353 475
[3]	Fu Z T, Chen Z, Zhang L N, Mao J Y and Liu S K 2010 Appl. Math. Comput. 215 3899
[4]	Sakovich A and Sakovich S 2005 J. Phys. Soc. Jpn. 74 239
[5]	Liu H, Li J and Liu L 2012 Stud. Appl. Math. 129 103
[6]	Olver P J 1993 Applications of Lie Groups to Differential Equations (New York: Springer-Verlag)
[7]	Wang X, Chen Y and Dong Z Z 2014 Chin. Phys. B 23 010201
[8]	Lou S Y, Hu X R and Chen Y 2012 J. Phys. A: Math. Theor. 45 155209
[9]	Song J F, Qu C Z and Qiao Z J 2011 J. Math. Phys. 52 013503
[10]	Su J R, Zhang S L and Li J N 2010 Commun. Theor. Phys. 53 37
[11]	Zhao G L, Chen L Q, Fu J L and Hong F Y 2013 Chin. Phys. B 22 030201
[12]	Sun X T, Han Y L, Wang X X, Zhang M L and Jia L Q 2012 Acta Phys. Sin. 61 200204 (in Chinese)
[13]	Bluman G W, Cheviakov A F and Anco S C 2010 Applications of Symmetry Methods to Partial Differential Equations (New York: Springer-Verlag)
[14]	Kara A H and Mahomed F M 2006 Nonlinear Dyn. 45 367
[15]	Naz R, Mahomed F M and Mason D P 2008 Appl. Math. Comput. 205 212
[16]	Gandarias M L 2014 Commun. Nonlinear Sci. Numer. Simul. 19 3523
[17]	Ibragimov N H 2011 Archives of ALGA 7/8 1
[18]	Zhang Z Y 2013 J. Phys. A: Math. Theor. 46 155203
[19]	Z Y and Chen Y F 2014 IMA J. Appl. Math. first published online May 8, 2014
[20]	Ibragimov N H 2007 J. Math. Anal. Appl. 333 311

[1]	Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws Xian-Guo Geng(耿献国), Fei-Ying Guo(郭飞英), Yun-Yun Zhai(翟云云). Chin. Phys. B, 2020, 29(5): 050201.
[2]	An extension of integrable equations related to AKNS and WKI spectral problems and their reductions Xian-Guo Geng(耿献国), Yun-Yun Zhai(翟云云). Chin. Phys. B, 2018, 27(4): 040201.
[3]	A local energy-preserving scheme for Zakharov system Qi Hong(洪旗), Jia-ling Wang(汪佳玲), Yu-Shun Wang(王雨顺). Chin. Phys. B, 2018, 27(2): 020202.
[4]	Residual symmetry, interaction solutions, and conservation laws of the (2+1)-dimensional dispersive long-wave system Ya-rong Xia(夏亚荣), Xiang-peng Xin(辛祥鹏), Shun-Li Zhang(张顺利). Chin. Phys. B, 2017, 26(3): 030202.
[5]	Local structure-preserving methods for the generalized Rosenau-RLW-KdV equation with power law nonlinearity Jia-Xiang Cai(蔡加祥), Qi Hong(洪旗), Bin Yang(杨斌). Chin. Phys. B, 2017, 26(10): 100202.
[6]	Conformal structure-preserving method for damped nonlinear Schrödinger equation Hao Fu(傅浩), Wei-En Zhou(周炜恩), Xu Qian(钱旭), Song-He Song(宋松和), Li-Ying Zhang(张利英). Chin. Phys. B, 2016, 25(11): 110201.
[7]	A new six-component super soliton hierarchy and its self-consistent sources and conservation laws Han-yu Wei(魏含玉) and Tie-cheng Xia(夏铁成). Chin. Phys. B, 2016, 25(1): 010201.
[8]	Multi-symplectic variational integrators for nonlinear Schrödinger equations with variable coefficients Cui-Cui Liao(廖翠萃), Jin-Chao Cui(崔金超), Jiu-Zhen Liang(梁久祯), Xiao-Hua Ding(丁效华). Chin. Phys. B, 2016, 25(1): 010205.
[9]	A local energy-preserving scheme for Klein–Gordon–Schrödinger equations Cai Jia-Xiang (蔡加祥), Wang Jia-Lin (汪佳玲), Wang Yu-Shun (王雨顺). Chin. Phys. B, 2015, 24(5): 050205.
[10]	Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term Cai Jia-Xiang (蔡加祥), Bai Chuan-Zhi (柏传志), Qin Zhi-Lin (秦志林). Chin. Phys. B, 2015, 24(10): 100203.
[11]	A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures Zhai Yun-Yun (翟云云), Geng Xian-Guo (耿献国), He Guo-Liang (何国亮). Chin. Phys. B, 2014, 23(6): 060201.
[12]	Riccati-type Bäcklund transformations of nonisospectral and generalized variable-coefficient KdV equations Yang Yun-Qing (杨云青), Wang Yun-Hu (王云虎), Li Xin (李昕), Cheng Xue-Ping (程雪苹). Chin. Phys. B, 2014, 23(3): 030506.
[13]	A conservative Fourier pseudospectral algorithm for the nonlinear Schrödinger equation Lv Zhong-Quan (吕忠全), Zhang Lu-Ming (张鲁明), Wang Yu-Shun (王雨顺). Chin. Phys. B, 2014, 23(12): 120203.
[14]	Symmetries and conservation laws of one Blaszak–Marciniak four-field lattice equation Wang Xin (王鑫), Chen Yong (陈勇), Dong Zhong-Zhou (董仲周). Chin. Phys. B, 2014, 23(1): 010201.
[15]	Multi-symplectic scheme for the coupled Schrödinger–Boussinesq equations Huang Lang-Yang (黄浪扬), Jiao Yan-Dong (焦艳东), Liang De-Min (梁德民). Chin. Phys. B, 2013, 22(7): 070201.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Conservation laws of the generalized short pulse equation

Cite this article:

Online attention