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With the help of the symbolic computation system Maple and Riccati equation (ξ’=a0+a1ξ+a2ξ2) expansion method and a variable separation method, some complex wave solutions with q=C1x+C2y+C3t+R(x,y,t) of the (2+1)-dimensional Korteweg-de Vries system is derived. Based on the derived solitary wave solution, some novel complex wave localized excitations such as complex wave fusion and complex wave annihilation are investigated.
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Keywords:
- Riccati equation expansion method /
- Korteweg-de Vries system /
- complex wave solutions /
- localized excitations
[1] Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[2] Tang X Y, Lou S Y, Zhang Y 2002 Phys. Rev. E 66 046601
[3] Lou S Y 1998 Phys. Rev. Lett. 80 5027
[4] Hietarinta J 1990 Phys. Lett. A 149 113
[5] Fokas A S 1998 Phys. Lett. A 132 432
[6] Zhang D J 2003 Chaos Soliton. Fract. 18 31
[7] Zhang D J 2005 Chaos Soliton. Fract. 23 1333
[8] Zhang S L, Zhu X N, Wang Y M, Lou S Y 2008 Commun. Theor. Phys. 49 829
[9] Zhang S L, Lou S Y 2007 Commun. Theor. Phys. 48 385
[10] Dai C Q, Zhou G Q 2007 Chin. Phys. B 16 1201
[11] Dai C Q, Ni Y Z 2006 Phys. Scripta 74 584
[12] Dai C Q, Zhu H P 2013 J. Opt. Soc. Am. B 30 3291
[13] Taogetusang, Sirendaoerji 2009 Acta Phys. Sin. 58 2121 (in Chinese) [套格图桑, 斯仁道尔吉 2009 58 2121]
[14] Taogetusang, Sirendaoerji 2009 Acta Phys. Sin. 58 5887 (in Chinese) [套格图桑, 斯仁道尔吉 2009 58 5887]
[15] Ma Y L, Li B Q, Sun J Z 2009 Acta Phys. Sin. 58 7402 (in Chinese) [马玉兰, 李帮庆, 孙践知 2009 58 7402]
[16] Mo J Q, Zhang W J, Chen X F 2009 Acta Phys. Sin. 58 7397 (in Chinese) [莫嘉琪, 张伟江, 陈贤峰 2009 58 7397]
[17] Zhang J F, Meng J P 2004 Commun. Theor. Phys. 41 655
[18] Zhang J F 2002 Commun. Theor. Phys. 37 277
[19] Lou S Y 1996 Commun. Theor. 26 487
[20] Lou S Y, Tang X Y, Li J 2001 Eue. Phys. J. B 22 473
[21] Fang J P, Zheng C L, Zhu J M 2005 Acta Phys. Sin. 54 2990 (in Chinese) [方建平, 郑春龙, 朱加民 2005 54 2990]
[22] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [方建平, 吴小红, 方建平, 郑春龙 2008 57 11]
[23] Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [马松华, 强继业, 方建平 2007 56 620]
[24] Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese) [马松华, 方建平 2006 55 5611]
[25] Fang J P, Zheng C L 2005 Chin. Phys. B 4 670
[26] Ma S H, Fang J P, Ren Q B, Yang Z 2012 Chin. Phys. B 21 050511
[27] Ma S H, Fang J P, Zheng C L 2009 Chaos Soliton. Fract. 40 210
[28] Ma S H, Fang J P, Ren Q B 2010 Acta Phys. Sin. 59 4420 (in Chinese) [马松华, 方建平, 任清褒 2010 59 4420]
[29] Ma S H, Fang J P, Wu H Y 2013 Z. Naturforsch. 68a 350
[30] Ma Z Y, Ma S H 2012 Chin. Phys. B 21 030507
[31] Chen Y M, Ma S H, Ma Z Y 2012 Chin. Phys. B 21 050510
[32] Lei Y, Ma S H, Fang J P 2013 Chin. Phys. B 22 010506
[33] Mei J Q, Zhang H Q 2005 Commun. Theor. Phys. (Beijing, China) 44 209
[34] Calogero F 1975 Lett. Nouvo Cimento. 14 443
[35] Lou S Y, Ruan H Y 2001 J. Phys. A 34 305
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[1] Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[2] Tang X Y, Lou S Y, Zhang Y 2002 Phys. Rev. E 66 046601
[3] Lou S Y 1998 Phys. Rev. Lett. 80 5027
[4] Hietarinta J 1990 Phys. Lett. A 149 113
[5] Fokas A S 1998 Phys. Lett. A 132 432
[6] Zhang D J 2003 Chaos Soliton. Fract. 18 31
[7] Zhang D J 2005 Chaos Soliton. Fract. 23 1333
[8] Zhang S L, Zhu X N, Wang Y M, Lou S Y 2008 Commun. Theor. Phys. 49 829
[9] Zhang S L, Lou S Y 2007 Commun. Theor. Phys. 48 385
[10] Dai C Q, Zhou G Q 2007 Chin. Phys. B 16 1201
[11] Dai C Q, Ni Y Z 2006 Phys. Scripta 74 584
[12] Dai C Q, Zhu H P 2013 J. Opt. Soc. Am. B 30 3291
[13] Taogetusang, Sirendaoerji 2009 Acta Phys. Sin. 58 2121 (in Chinese) [套格图桑, 斯仁道尔吉 2009 58 2121]
[14] Taogetusang, Sirendaoerji 2009 Acta Phys. Sin. 58 5887 (in Chinese) [套格图桑, 斯仁道尔吉 2009 58 5887]
[15] Ma Y L, Li B Q, Sun J Z 2009 Acta Phys. Sin. 58 7402 (in Chinese) [马玉兰, 李帮庆, 孙践知 2009 58 7402]
[16] Mo J Q, Zhang W J, Chen X F 2009 Acta Phys. Sin. 58 7397 (in Chinese) [莫嘉琪, 张伟江, 陈贤峰 2009 58 7397]
[17] Zhang J F, Meng J P 2004 Commun. Theor. Phys. 41 655
[18] Zhang J F 2002 Commun. Theor. Phys. 37 277
[19] Lou S Y 1996 Commun. Theor. 26 487
[20] Lou S Y, Tang X Y, Li J 2001 Eue. Phys. J. B 22 473
[21] Fang J P, Zheng C L, Zhu J M 2005 Acta Phys. Sin. 54 2990 (in Chinese) [方建平, 郑春龙, 朱加民 2005 54 2990]
[22] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [方建平, 吴小红, 方建平, 郑春龙 2008 57 11]
[23] Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [马松华, 强继业, 方建平 2007 56 620]
[24] Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese) [马松华, 方建平 2006 55 5611]
[25] Fang J P, Zheng C L 2005 Chin. Phys. B 4 670
[26] Ma S H, Fang J P, Ren Q B, Yang Z 2012 Chin. Phys. B 21 050511
[27] Ma S H, Fang J P, Zheng C L 2009 Chaos Soliton. Fract. 40 210
[28] Ma S H, Fang J P, Ren Q B 2010 Acta Phys. Sin. 59 4420 (in Chinese) [马松华, 方建平, 任清褒 2010 59 4420]
[29] Ma S H, Fang J P, Wu H Y 2013 Z. Naturforsch. 68a 350
[30] Ma Z Y, Ma S H 2012 Chin. Phys. B 21 030507
[31] Chen Y M, Ma S H, Ma Z Y 2012 Chin. Phys. B 21 050510
[32] Lei Y, Ma S H, Fang J P 2013 Chin. Phys. B 22 010506
[33] Mei J Q, Zhang H Q 2005 Commun. Theor. Phys. (Beijing, China) 44 209
[34] Calogero F 1975 Lett. Nouvo Cimento. 14 443
[35] Lou S Y, Ruan H Y 2001 J. Phys. A 34 305
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