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We propose a method of obtaining peakon solution from bell-shape smooth soliton (or solitary wave)solution, i.e. constructing directly an ansatz solution of peakon according to the well-known bell-shape smooth soliton solution and then determining the coefficients in ansatz solution. The method is verified to be feasible for four nonlinear wave equations and one set of equations. The bell-shape smooth soliton (or solitary wave)solution and peakon solution can exist in the same expression and the expressions of peakon solutions include those of the bell-shape smooth soliton solutions and the latter are the special cases of the former.
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Keywords:
- nonlinear wave equation /
- bell-shape smooth soliton(or solitary wave) solution /
- peaked soliton (peakon)solution
[1] Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[2] [3] Liu Z R, Qian T F 2002 Appl. Math. Model. 26 473
[4] [5] Qiao Z J, Zhang G P 2006 Europhys. Lett. 73 657
[6] Liu Z R 2004 J. Yunnan Nationalities Univ. (Nat. Sci. Ed.) 13 3 (in Chinese)[刘正荣 2004 云南民族大学学报(自然科学版) 13 3]
[7] [8] Yu L Q, Tian L X 2006 Math. Prac. Theor. 36 261(in Chinese)[余丽琴、田立新 2006 数学的实践与认识 36 261]
[9] [10] Yu L Q, Tian L X 2005 Pure Appl. Math. 21 310 (in Chinese)[余丽琴、田立新 2005 纯粹数学与应用数学 21 310]
[11] [12] [13] Guo B L, Liu Z R 2003 Sci. China A 33 325(in Chinese)[郭柏灵、刘正荣 2003 中国科学 A 33 325]
[14] Xie S L 2001 J. Yunnan Univ. (Nat. Sci. Ed.) 23 5(in Chinese)[谢绍龙 2001 云南大学学报(自然科学版) 23 5]
[15] [16] Song X Y, Tian L X 2003 J. Jiangsu Univ. (Nat. Sci. Ed.) 24 35(in Chinese)[宋秀迎、田立新 2003 江苏大学学报(自然科学版) 24 35]
[17] [18] Liu Z R, Yang X Y 2007 J. Yunnan Nationalities Univ. (Nat. Sci. Ed.) 16 89 (in Chinese)[刘正荣、杨喜艳 2007 云南民族大学学报(自然科学版) 16 89]
[19] [20] Liu Y 2009 Acta Phys. Sin. 58 7452(in Chinese)[刘 煜 2009 物理学报 58 7452]
[21] [22] Liu S K, Liu S D 2000 Nonlinear Equation in Physics (Beijing: Peking University Press) pp176, 177, 187, 188, 190, 191(in Chinese) [刘式适、刘式达 2000 物理学中的非线性方程(北京:北京大学出版社) 第176, 177, 187, 188, 190, 191页]
[23] [24] [25] Qimusurong, Wuenbaoyin 1997 J. Inner Mongolia Teacher Col. Nationalities (Nat. Sci. Ed.) 12 158 (in Chinese)[其木苏荣、乌恩宝音 1997 内蒙古民族师院学报(自然科学版) 12 158]
[26] [27] Chen J L, Li X Z, Wang Y M 2005 J. Lanzhou Univ. Techn. (Nat. Sci. Ed.) 31 140 (in Chinese)[陈金兰、李向正、王跃明 2005 兰州理工大学学报(自然科学版) 31 140]
[28] Li H, Sun S R, Li J B 2006 Appl. Math. Comput. 175 61
[29] [30] Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 6214(in Chinese)[套格图桑、斯仁道尔吉 2006 物理学报 55 6214]
[31] [32] Guo G P,Zhang J F 2002 Acta Phys. Sin. 51 1159 (in Chinese)[郭冠平、张解放 2002 物理学报 51 1159]
[33] [34] Lin J, Wang R M, Ye L J 2006 Chin. Phys. 15 665
[35] -
[1] Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[2] [3] Liu Z R, Qian T F 2002 Appl. Math. Model. 26 473
[4] [5] Qiao Z J, Zhang G P 2006 Europhys. Lett. 73 657
[6] Liu Z R 2004 J. Yunnan Nationalities Univ. (Nat. Sci. Ed.) 13 3 (in Chinese)[刘正荣 2004 云南民族大学学报(自然科学版) 13 3]
[7] [8] Yu L Q, Tian L X 2006 Math. Prac. Theor. 36 261(in Chinese)[余丽琴、田立新 2006 数学的实践与认识 36 261]
[9] [10] Yu L Q, Tian L X 2005 Pure Appl. Math. 21 310 (in Chinese)[余丽琴、田立新 2005 纯粹数学与应用数学 21 310]
[11] [12] [13] Guo B L, Liu Z R 2003 Sci. China A 33 325(in Chinese)[郭柏灵、刘正荣 2003 中国科学 A 33 325]
[14] Xie S L 2001 J. Yunnan Univ. (Nat. Sci. Ed.) 23 5(in Chinese)[谢绍龙 2001 云南大学学报(自然科学版) 23 5]
[15] [16] Song X Y, Tian L X 2003 J. Jiangsu Univ. (Nat. Sci. Ed.) 24 35(in Chinese)[宋秀迎、田立新 2003 江苏大学学报(自然科学版) 24 35]
[17] [18] Liu Z R, Yang X Y 2007 J. Yunnan Nationalities Univ. (Nat. Sci. Ed.) 16 89 (in Chinese)[刘正荣、杨喜艳 2007 云南民族大学学报(自然科学版) 16 89]
[19] [20] Liu Y 2009 Acta Phys. Sin. 58 7452(in Chinese)[刘 煜 2009 物理学报 58 7452]
[21] [22] Liu S K, Liu S D 2000 Nonlinear Equation in Physics (Beijing: Peking University Press) pp176, 177, 187, 188, 190, 191(in Chinese) [刘式适、刘式达 2000 物理学中的非线性方程(北京:北京大学出版社) 第176, 177, 187, 188, 190, 191页]
[23] [24] [25] Qimusurong, Wuenbaoyin 1997 J. Inner Mongolia Teacher Col. Nationalities (Nat. Sci. Ed.) 12 158 (in Chinese)[其木苏荣、乌恩宝音 1997 内蒙古民族师院学报(自然科学版) 12 158]
[26] [27] Chen J L, Li X Z, Wang Y M 2005 J. Lanzhou Univ. Techn. (Nat. Sci. Ed.) 31 140 (in Chinese)[陈金兰、李向正、王跃明 2005 兰州理工大学学报(自然科学版) 31 140]
[28] Li H, Sun S R, Li J B 2006 Appl. Math. Comput. 175 61
[29] [30] Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 6214(in Chinese)[套格图桑、斯仁道尔吉 2006 物理学报 55 6214]
[31] [32] Guo G P,Zhang J F 2002 Acta Phys. Sin. 51 1159 (in Chinese)[郭冠平、张解放 2002 物理学报 51 1159]
[33] [34] Lin J, Wang R M, Ye L J 2006 Chin. Phys. 15 665
[35]
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