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Chin. Phys. B, 2017, Vol. 26(3): 030202    DOI: 10.1088/1674-1056/26/3/030202
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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 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
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

[1] Hasegawa A 1989 Optical Solitons in Fibers (Berlin: Springer-Verlag)
[2] Wang L, Sun Z Y, Qi F H, Meng D X and Lin G D 2012 Nonlin. Dyn. 67 713
[3] Bekir A and Guner O 2016 Chin. Phys. B 25 030203
[4] Chen C L, Lou S Y and Li Y S 2004 Commun. Nonlinear Sci. Numer. Simul. 9 583
[5] Chen C L and Lou S Y 2003 Chaos Soliton Fract. 16 27
[6] Liu P, Zeng B Q, Yang J R and Ren B 2015 Chin. Phys. B 24 010202
[7] Xin X P and Chen Y 2013 Chin. Phys. lett. 30 100202
[8] Huang L L and Chen Y 2016 Chin. Phys. B 6 060201
[9] Guthrie G A 1994 Proc. R Soc. Lond. Ser. A 446 107
[10] Lou S Y 1994 J. Math. Phys. 35 2390
[11] Lou S Y and Hu X B 1997 J. Phys. A: Math Gen. 30 L95
[12] Chen J C, Xin X P and Chen Y 2014 J. Math. Phys. 55 053508
[13] Lou S Y, Hu X R and Chen Y 2012 J. Phys. A: Math. Theor. 45 155209
[14] Xin X P, Miao Q and Chen Y 2014 Chin. Phys. B 23 110203
[15] Lou S Y 1997 J. Phys. A: Math. Phys. 30 4803
[16] Lou S Y 1998 Phys. Scr. 57 481
[17] Gao X N, Lou S Y and Tang X Y 2013 J. High Energy Phys. 5 029
[18] Lou S Y 2013 arxiv:1308.1140v1 [nlin.SI]
[19] Xin X P, Liu Y T and Liu X Q 2016 Appl. Math. Lett. 55 63
[20] Lou S Y 2013 arxiv:1308.5891v2 [nlin.SI]
[21] Chen C L and Lou S Y 2014 Commun. Theor. Phys. 61 545
[22] Adem A R, Khalique C M 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3465
[23] Noether E 1918 Math.Phys. Kl. Heft. 2 235
[24] Ibragimov N H 2007 J. Math. Anal. Appl. 333 311
[25] Ibragimov N H 2011 Arch. ALGA. 7 1
[26] Gandarias M L 2011 J. Phys A: Math. Theor. 44 262001.
[27] Ibragimov N H, Torrisi M and Traciná R 2011 J. Phys. A: Math. Theor. 44 145201
[28] Boiti M, Leon J J P and Pempinelli F 1987 Inverse Probl. 3 371
[29] Zeng X and Zhang H Q 2005 Acta Phys. Sin. 54 504
[30] Zhou Y Q, Liu Q, Zhang J and Zhang W N 2006 Appl. Math. Comput. 177 495
[31] Zheng C L, Fang J P and Chen L Q 2005 Chaos Soliton Fract. 23 1741
[32] Tang X Y and Lou S Y 2002 Chaos Soliton Fract. 14 1451
[33] Estévez P G and Gordoa P R 1997 Inverse Probl. 13 939
[34] Wen X Y 2012 Rep. math. phys. 69 197
[35] Olver P J 1986 Applications of Lie Group to Differential Equations (New York: Spring-Verlag)
[36] Yu W F, Lou S Y, Yu J and Yang D 2014 Commun. Theor. Phys. 62 297
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