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Using the CK direct method, we obtain the similarity reduction of coupled KdV equation, which is then explained in detail by group theory. To check the Painlev integrability of coupled KdV equation, the reduction equation is also classified by means of the Painlev test, and three types of P-integrable models are found. Finally, it is shown that the coupled KdV equation has kinds of traveling wave solutions, including conoidal periodic wave solution, soliton solution, and so on.
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Keywords:
- coupled KdV equation /
- CK direct method /
- Painlev test /
- exact analytical solution
[1] Li Z B, Pan S Q 2001 Acta Phys.Sin.50 402 (in Chinese)[李志斌、潘素起 2001 物理学报 50 402]
[2] Mao J J, Yang J R 2007 Acta Phys.Sin. 56 5049 (in Chinese)[毛杰健、杨建荣 2007 物理学报 56 5049]
[3] [4] Hirota R, Satsuma J 1981 Phys.Lett. A 85 407
[5] [6] [7] Lou S Y, Tong B, Hu H C, Tang X Y 2006 J.Phys.A: Math.Gen. 39 513
[8] [9] Hu H C, Tong B, Lou S Y 2006 Phys.Lett. A 351 403
[10] [11] Shi Y R, Zhang J, Yang H J, Duan W S 2011 Acta Phys.Sin. 60 020401 (in Chinese)[石玉仁、张 娟、杨红娟、段文山 2011 物理学报 60 020401]
[12] [13] Tong B, Jia M, Lou S Y 2006 Commun.Theor.Phys. 45 965
[14] Jia M 2008 Commun.Theor.Phys. 49 275
[15] [16] [17] Gear J A, Grimshaw R 1984 Stud.Appl.Math. 70 235
[18] Tang X Y, Huang F, Lou S Y 2006 Chin.Phys.Lett. 23 887
[19] [20] [21] Liu X Z 2010 Chin.Phys. B 19 080202
[22] [23] Liu D B, Chu K Q 2001 Chin.Phys. 10 683
[24] Lou S Y, Tang X Y 2006 Nonlinear Mathematical Physics Method(Beijing: Science Press)p314(in Chinese)[楼森岳、唐晓艳 2006 非线性数学物理方法.(北京:科学出版社)第314页]
[25] [26] [27] Ruan H Y, Li H J 2005 Acta Phys.Sin. 54 996 (in Chinese)[阮航宇、李慧军 2005 物理学报 54 996]
[28] Lou S Y, Ni G J 1989 J.Math.Phys. 30 1614
[29] -
[1] Li Z B, Pan S Q 2001 Acta Phys.Sin.50 402 (in Chinese)[李志斌、潘素起 2001 物理学报 50 402]
[2] Mao J J, Yang J R 2007 Acta Phys.Sin. 56 5049 (in Chinese)[毛杰健、杨建荣 2007 物理学报 56 5049]
[3] [4] Hirota R, Satsuma J 1981 Phys.Lett. A 85 407
[5] [6] [7] Lou S Y, Tong B, Hu H C, Tang X Y 2006 J.Phys.A: Math.Gen. 39 513
[8] [9] Hu H C, Tong B, Lou S Y 2006 Phys.Lett. A 351 403
[10] [11] Shi Y R, Zhang J, Yang H J, Duan W S 2011 Acta Phys.Sin. 60 020401 (in Chinese)[石玉仁、张 娟、杨红娟、段文山 2011 物理学报 60 020401]
[12] [13] Tong B, Jia M, Lou S Y 2006 Commun.Theor.Phys. 45 965
[14] Jia M 2008 Commun.Theor.Phys. 49 275
[15] [16] [17] Gear J A, Grimshaw R 1984 Stud.Appl.Math. 70 235
[18] Tang X Y, Huang F, Lou S Y 2006 Chin.Phys.Lett. 23 887
[19] [20] [21] Liu X Z 2010 Chin.Phys. B 19 080202
[22] [23] Liu D B, Chu K Q 2001 Chin.Phys. 10 683
[24] Lou S Y, Tang X Y 2006 Nonlinear Mathematical Physics Method(Beijing: Science Press)p314(in Chinese)[楼森岳、唐晓艳 2006 非线性数学物理方法.(北京:科学出版社)第314页]
[25] [26] [27] Ruan H Y, Li H J 2005 Acta Phys.Sin. 54 996 (in Chinese)[阮航宇、李慧军 2005 物理学报 54 996]
[28] Lou S Y, Ni G J 1989 J.Math.Phys. 30 1614
[29]
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