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利用Clarkson和Kruskal(CK)直接方法,对耦合KdV方程进行相似约化,同时从李群出发对该约化方程作了群论解释.进一步地,借助Ablowitz-Ramani-Segur(ARS)算法对耦合方程展开Painlev测试,找到了3个Painlev可积模型.最后通过形变映射法,求得耦合KdV方程的准确解析解.
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关键词:
- 耦合KdV方程 /
- CK直接法 /
- Painlev分析法 /
- 准确解析解
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.-
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 50 402]
[2] Mao J J, Yang J R 2007 Acta Phys.Sin. 56 5049 (in Chinese)[毛杰健、杨建荣 2007 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 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 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 50 402]
[2] Mao J J, Yang J R 2007 Acta Phys.Sin. 56 5049 (in Chinese)[毛杰健、杨建荣 2007 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 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 54 996]
[28] Lou S Y, Ni G J 1989 J.Math.Phys. 30 1614
[29]
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