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利用改进的 Riccati方程映射法和变量分离法, 得到了扩展的(2+1)维浅水波方程的变量分离解(包括孤波解, 周期波解和有理函数解). 根据得到的孤波解, 构造出了方程的几种不同形状的尖峰孤子结构, 研究了孤子的相互作用.
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关键词:
- 改进的映射法 /
- 扩展的(2+1)维浅水波方程 /
- 尖峰孤子 /
- 相互作用
By an improved Riccati mapping approach and a variable separation approach, a new family of variable separation solutions (including solitory wave solutions, periodic wave solutions, and rational function solutions) of the extended (2+1)-dimensional shallow water wave (SWW) equation is derived. According to the derived solitary wave excitation, we obtain some special peaked soliton structures and study the interaction between solitons.-
Keywords:
- improved mapping approach /
- extended (2+1)-dimensional shallow water wave equation /
- peaked soliton /
- interaction between solitons
[1] Li B Q, Ma Y L 2010 Z. Naturforsch. 65a 518
[2] Ma Y L, Li B Q 2010 J. Math. Phys. 51 063512
[3] 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 ]
[4] Li B Q, Ma Y L, Xu M P 2010 Acta Phys. Sin. 59 1409 (in Chinese) [李帮庆, 马玉兰, 徐美萍 2010 59 1409 ]
[5] Hietarinta J 1990 Phys. Lett. A 149 113
[6] Radha R, Lakshmanan M 1991 Phys. Lett. A 197 7
[7] Lou S Y 1995 J. Phys. Math. Gen. A 28 7227
[8] Ruan H Y, Lou S Y 1997 J. Math. Phys. 38 3123
[9] Lou S Y 1996 Commun. Theor. 26 487
[10] Lou S Y, Tang X Y, Li J 2001 Eue. Phys. J. B 22 473
[11] Lai D W C, Chow K W 1999 J. Phys. Soc. Jpn. 65 1847
[12] Lai D W C, Chow K W 2001 J. Phys. Soc. Jpn. 70 666
[13] Fang J P, Zheng C L, Chen L Q 2004 Commun. Theor. Phys. 42 175
[14] 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 ]
[15] Lü Z S, Zhang H Q 2004 Chaos, Solitons and Fractals 19 527
[16] Fang J P, Zheng C L 2005 Chin. Phys. 4 670
[17] Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese) [马松华, 方建平 2006 55 5611 ]
[18] Ma S H, Fang J P, Hong B H, Zheng C L 2009 Chaos, Solitons and Fractals 40 1352
[19] Yang Z, Ma S H, Fang J P 2011 Chin. Phys. B 20 040301
[20] 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]
[21] 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 ]
[22] Boiti M, Leon J J, Manna M, Pempinelli F 1989 Phys. Rev. Lett. A 63 1329
[23] Zhang J F, Huang W H, Zheng C L 2002 Acta Phys. Sin. 51 2676 (in Chinese) [张解放, 黄文华, 郑春龙 2002 51 2676]
[24] Zhang S L, Zhu X N, Wang Y M, Lou S Y 2008 Commun. Theor. Phys. 49 829
[25] Zhang S L, Lou S Y 2007 Commun. Theor. Phys. 48 385
[26] Zhang J F, Meng J P 2004 Commun. Theor. Phys. 41 655
[27] Lou S Y 2003 J. Phys. A Math. Gen. 36 3877
[28] Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese) [莫嘉琪 2009 58 695]
[29] Dai C Q, Yan C J, Zhang J F 2006 Commun. Theor. Phys. 46 389
[30] Zheng C L, Fang J P, Chen L Q 2005 Acta Phys. Sin. 54 1468 (in Chinese) [郑春龙, 方建平, 陈立群 2005 54 1468]
[31] Wazwaz A M 2010 Studies in Mathematical Sciences 1 21
[32] Wang Y H, Chen Y 2011 Commun. Theor. Phys. 56 672
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[1] Li B Q, Ma Y L 2010 Z. Naturforsch. 65a 518
[2] Ma Y L, Li B Q 2010 J. Math. Phys. 51 063512
[3] 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 ]
[4] Li B Q, Ma Y L, Xu M P 2010 Acta Phys. Sin. 59 1409 (in Chinese) [李帮庆, 马玉兰, 徐美萍 2010 59 1409 ]
[5] Hietarinta J 1990 Phys. Lett. A 149 113
[6] Radha R, Lakshmanan M 1991 Phys. Lett. A 197 7
[7] Lou S Y 1995 J. Phys. Math. Gen. A 28 7227
[8] Ruan H Y, Lou S Y 1997 J. Math. Phys. 38 3123
[9] Lou S Y 1996 Commun. Theor. 26 487
[10] Lou S Y, Tang X Y, Li J 2001 Eue. Phys. J. B 22 473
[11] Lai D W C, Chow K W 1999 J. Phys. Soc. Jpn. 65 1847
[12] Lai D W C, Chow K W 2001 J. Phys. Soc. Jpn. 70 666
[13] Fang J P, Zheng C L, Chen L Q 2004 Commun. Theor. Phys. 42 175
[14] 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 ]
[15] Lü Z S, Zhang H Q 2004 Chaos, Solitons and Fractals 19 527
[16] Fang J P, Zheng C L 2005 Chin. Phys. 4 670
[17] Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese) [马松华, 方建平 2006 55 5611 ]
[18] Ma S H, Fang J P, Hong B H, Zheng C L 2009 Chaos, Solitons and Fractals 40 1352
[19] Yang Z, Ma S H, Fang J P 2011 Chin. Phys. B 20 040301
[20] 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]
[21] 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 ]
[22] Boiti M, Leon J J, Manna M, Pempinelli F 1989 Phys. Rev. Lett. A 63 1329
[23] Zhang J F, Huang W H, Zheng C L 2002 Acta Phys. Sin. 51 2676 (in Chinese) [张解放, 黄文华, 郑春龙 2002 51 2676]
[24] Zhang S L, Zhu X N, Wang Y M, Lou S Y 2008 Commun. Theor. Phys. 49 829
[25] Zhang S L, Lou S Y 2007 Commun. Theor. Phys. 48 385
[26] Zhang J F, Meng J P 2004 Commun. Theor. Phys. 41 655
[27] Lou S Y 2003 J. Phys. A Math. Gen. 36 3877
[28] Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese) [莫嘉琪 2009 58 695]
[29] Dai C Q, Yan C J, Zhang J F 2006 Commun. Theor. Phys. 46 389
[30] Zheng C L, Fang J P, Chen L Q 2005 Acta Phys. Sin. 54 1468 (in Chinese) [郑春龙, 方建平, 陈立群 2005 54 1468]
[31] Wazwaz A M 2010 Studies in Mathematical Sciences 1 21
[32] Wang Y H, Chen Y 2011 Commun. Theor. Phys. 56 672
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