Residual symmetry, interaction solutions, and conservation laws of the (2+1)-dimensional dispersive long-wave system

doi:10.1088/1674-1056/26/3/030202

Abstract We explore the (2+1)-dimensional dispersive long-wave (DLW) system. From the standard truncated Painlevé expansion, the Bäcklund transformation (BT) and residual symmetries of this system are derived. The introduction to an appropriate auxiliary dependent variable successfully localizes the residual symmetries to Lie point symmetries. In particular, it is verified that the (2+1)-dimensional DLW system is consistent Riccati expansion (CRE) solvable. If the special form of (CRE)-consistent tanh-function expansion (CTE) is taken, the soliton-cnoidal wave solutions and corresponding images can be explicitly given. Furthermore, the conservation laws of the DLW system are investigated with symmetries and Ibragimov theorem.

Keywords: residual symmetry truncated Painlevé expansion interaction solutions conservation law

Received: 20 August 2016
Revised: 06 November 2016
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	04.20.Jb	(Exact solutions)
	11.10.Lm	(Nonlinear or nonlocal theories and models)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11371293 and 11505090), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2014JM2-1009), the Research Award Foundation for Outstanding Young Scientists of Shandong Province, China (Grant No. BS2015SF009), and the Science and Technology Innovation Foundation of Xi'an, China (Grant No. CYX1531WL41).

Corresponding Authors: Xiang-peng Xin
E-mail: xinxiangpeng2012@gmail.com

Cite this article:

Ya-rong Xia(夏亚荣), Xiang-peng Xin(辛祥鹏), Shun-Li Zhang(张顺利) Residual symmetry, interaction solutions, and conservation laws of the (2+1)-dimensional dispersive long-wave system 2017 Chin. Phys. B 26 030202

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Residual symmetry, interaction solutions, and conservation laws of the (2+1)-dimensional dispersive long-wave system

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