Chin. Phys. Lett.  2010, Vol. 27 Issue (9): 090201    DOI: 10.1088/0256-307X/27/9/090201
GENERAL |
New Type Soliton Solutions to Korteweg-de Vries and Benjamin-Bona-Mahony Equations
LIU Yu
Henan Electric Power Research Institute, Zhengzhou 450052
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LIU Yu 2010 Chin. Phys. Lett. 27 090201
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Abstract

We study the Korteweg-de Vries equation and the Benjamin-Bona-Mahony equation, and obtain three kinds of new type soliton solutions, i.e. peakon solutions, double-peak (peaked-point and peaked-compacton) soliton solutions. A double solitary wave with blow-up points is also contained.

Keywords: 02.30.Jr      05.45.Yv     
Received: 17 March 2010      Published: 25 August 2010
PACS:  02.30.Jr (Partial differential equations)  
  05.45.Yv (Solitons)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/27/9/090201       OR      https://cpl.iphy.ac.cn/Y2010/V27/I9/090201
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LIU Yu

[1] Camassa R and Holm D D 1993 Phys. Rev. Lett. 71 1661
[2] Rosenau P and Hyman J M 1993 Phys. Rev. Lett. 70 564
[3] Liu Z R and Qian T F 2002 Appl. Math. Modeling 26 473
[4] Liu Z R 2004 J. Yunnan Nationalities University (NSE) 13 3 (in Chinese)
[5] Yu L Q and Tian L X 2006 Mathematics in Practice and Theory 36 261 (in Chinese)
[6] Shen J W and Xu W 2005 J. Taiyuan University of Technology (NSE) 36 742 (in Chinese)
[7] Yu L Q and Tian L X 2005 J. Engin. Math. 22 1133 (in Chinese)
[8] Yu L Q and Tian L X 2005 Pure and Applied Mathematics 21 310 (in Chinese)
[9] Guo B Land Liu Z R 2003 Science in China (Ser.A) 33 325 (in Chinese)
[10] Xie S L 2001 Journal of Yunnan University (NSE) 23 5 (in Chinese)
[11] Song X Y and Tian L X 2003 Journal of Jiangsu University (NSE) 24 35 (in Chinese)
[12] Liu Z R and Yang X Y 2007 Journal of Yunnan Nationalities University (NSE) 16 89 (in Chinese)
[13] Dey B 1998 Phys. Rev. E 57 4733
[14] Yan Z Y 2002 Chaos, Solitons and Fractals 14 1151
[15] Wazwaz A M 2006 Physica A 371 273
[16] Wazwaz A M 2007 Appl. Math. Comput. 188 1930
[17] Feng D H, Li J B, Lv J L and He T L 2008 Appl. Math. Comput. 198 715
[18] Yin J L and Tian L X 2004 Acta Phys. Sin. 53 2821 (in Chinese)
[19] Liu Y 2009 Acta Phys. Sin. 58 7452(in Chinese)
[20] Liu S K and Liu S D 2000 Nonlinear Equation in Physics (Beijing: Peking University Press) p 190 (in Chinese)
[21] Chen S L and Hou W G 2001 Acta Phys. Sin. 50 1842 (in Chinese)
[22] Liu S K, Chen H, Fu Z T and Liu S D 2003 Acta Phys. Sin. 52 1842 (in Chinese)
[23] Taogetusang and Sirendaoerji 2006 Acta Phys. Sin. 55 6214 (in Chinese)
[24] Taogetusang and Sirendaoerji 2004 Acta Phys. Sin. 53 4052 (in Chinese)

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