中国物理B ›› 2017, Vol. 26 ›› Issue (3): 30202-030202.doi: 10.1088/1674-1056/26/3/030202

• GENERAL • 上一篇    下一篇

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)   

  1. 1 Center for Nonlinear Studies, School of Mathematics, Northwest University, Xi'an 710069, China;
    2 School of Information and Engineering, Xi'an University, Xi'an 710065, China;
    3 School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China
  • 收稿日期:2016-08-20 修回日期:2016-11-06 出版日期:2017-03-05 发布日期:2017-03-05
  • 通讯作者: Xiang-peng Xin E-mail:xinxiangpeng2012@gmail.com
  • 基金资助:
    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).

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

Ya-rong Xia(夏亚荣)1,2, Xiang-peng Xin(辛祥鹏)3, Shun-Li Zhang(张顺利)1   

  1. 1 Center for Nonlinear Studies, School of Mathematics, Northwest University, Xi'an 710069, China;
    2 School of Information and Engineering, Xi'an University, Xi'an 710065, China;
    3 School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China
  • Received:2016-08-20 Revised:2016-11-06 Online:2017-03-05 Published:2017-03-05
  • Contact: Xiang-peng Xin E-mail:xinxiangpeng2012@gmail.com
  • Supported by:
    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).

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摘要： 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.

关键词: residual symmetry, truncated Painlevé, expansion, interaction solutions, conservation law

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.

Key words: residual symmetry, truncated Painlevé, expansion, interaction solutions, conservation law

中图分类号:  (Partial differential equations)

  • 02.30.Jr
04.20.Jb (Exact solutions) 11.10.Lm (Nonlinear or nonlocal theories and models)