-
将(G′/G)展开法扩展到研究高维非线性物理方程的非行波解和分形结构. 以(2+1)维变系数色散长波系统为例, 构造出该系统的非行波解, 对解中的任意函数进行适当的设置, 发现了一类新的分形结构, 即十字形分形结构.
-
关键词:
- (G′/G)展开法 /
- (2+1)维变系数色散长波系统 /
- 非行波解 /
- 十字形分形结构
The (G′/G)-expansion method is extended to construct non-traveling wave solutions and explore the fractal structure for high dimensional nonlinear physical equation. As an example, a series of non-traveling solutions is obtained for the (2+1)-dimensional dispersive long wave system with variable coefficient. Furthermore, by setting properly the arbitrary functions in the solutions, a class of novel fractal structures, namely, the cross-like fractal structures are firstly observed.-
Keywords:
- (G′/G)-expansion method /
- (2+1)-dimensional dispersive long wave system with variable coefficient /
- non-traveling solution /
- cross-like fractal structure
[1] [1]Wang M L 1995 Phys. Lett. A 199 169
[2] [2]Yan Z Y, Zhang H Q 2000 Acta Phys. Sin. 49 2113 (in Chinese)[闫振亚、张鸿庆 2000 物理学报 49 2113]
[3] [3]Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese)[范恩贵2000 物理学报 49 1409]
[4] [4]Liu S K, Liu S D, Fu Z T 2001 Acta Phys. Sin. 50 2068 (in Chinese)[刘式适、刘适达、付遵涛 2001 物理学报 50 2068]
[5] [5]Liu S D, Fu Z T, Liu S K, Zhao Q 2002 Acta Phys. Sin. 51 718 (in Chinese)[刘式达、付遵涛、刘适式、赵强 2002 物理学报 51 718 ]
[6] [6]Wu G J, Han J H, Shi L M, Zhang M 2006 Acta Phys. Sin. 55 3858 (in Chinese)[吴国将、韩家骅、史良马、张苗 2006 物理学报 55 3858 ]
[7] [7]Wang M L, Zhou Y B, Li Z B 2003 Phys. Lett. A 318 84
[8] [8]Zhou Y B, Wang ML, Miao T D 2004 Phys. Lett. A 323 77
[9] [9]Zhang J L,Wang Y M,Wang M L 2003 Acta Phys. Sin. 52 1574 (in Chinese)[张金良、王跃明、王明亮 2003物理学报 52 1574]
[10] [10]Li X Z, Zhang J L, Wang Y M, Wang M L 2004 Acta Phys. Sin. 53 4045 (in Chinese)[李向正、张金良、王跃明、王明亮 2004 物理学报 53 4045]
[11] [11]Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 13 (in Chinese)[套格图桑、斯仁道尔吉 2006 物理学报 55 13]
[12] [12]Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese)[套格图桑、斯仁道尔吉 2006 物理学报 55 3246]
[13] [13]Li X Z, Li X Y, Zhao L Y, Zhang J L 2008 Acta Phys. Sin. 57 2203 (in Chinese)[李向正、李修勇、赵丽英、张金良 2008 物理学报 57 2203]
[14] [14]Ma Y L, Li B Q 2009 Appl. Math. Comput. 211 102
[15] [15]Lou S Y, Qu C Z, Zhang S L 2006 Chin. Phys. 15 2765
[16] [16]Tang X Y, Liang Z F 2006 Phys. Lett. A 351 398
[17] [17]Zhang S L, Lou S Y, Qu C Z 2006 Chin. Phys. 15 2765
[18] [18]Ma H C, Ge D J, Yu Y D 2008 Chin. Phys. B 17 1448
[19] [19]Ying J P, Lou S Y 2003 Chin. Phys. Lett. 20 1448
[20] [20]Fang J P, Zheng C L, Zhu J M 2005 Commun. Theor. Phys. 44 203
[21] [21]Fang J P, Zheng C L 2005 Chin. Phys. 14 670
[22] [22]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 物理学报 54 2990]
[23] [23]Ma S H, Wu X H, Fang J P, Zheng C L 2006 Z. Naturforsch. 61a 249
[24] [24]Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese)[马松华、方建平 2006 物理学报 55 5611]
[25] [25]Ma S H, Fang J P, Zheng C L 2008 Chin. Phys. B 17 2767
[26] [26]Ma S H, Fang J P,Hong B H, Zheng C L 2008 Commun. Theor. Phys. 49 1245
[27] [27]Huang L, Sun J A, Dou F Q, Duan W S, Liu X X 2007 Acta Phys. Sin. 56 611 (in Chinese)[黄磊、孙建安、豆福全、段文山 2007 物理学报 56 611]
[28] [28]Ma S H, Fang J P, Zheng C L 2007 Z. Naturforsch. 62a 8
[29] [29]Ma S H, Fang J P, Zheng C L 2008 Z. Naturforsch. 63a 121
[30] [30]Li J B, Zheng C L, Ma S H 2008 Z. Naturforsch. 63a 641
[31] [31]Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 0011 (in Chinese)[马松华、吴小红、方建平、郑春龙 2008 物理学报 57 0011]
[32] [32]Lou S Y, Tang X Y 2006 Methods of Nonlinear Mathematical Physics(Beijing: Science Press) p120(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120页]
[33] [33]Ma Z Y, Zhu J M, Zheng C L 2004 Chin. Phys. 13 1382
[34] [34]Zhu J M, Ma Z Y, Zheng C L 2004 Acta Phys. Sin. 53 3248 (in Chinese)[朱加民、马正义、郑春龙 2004 物理学报 53 3248]
[35] [35] Ma Z Y, Zheng C L 2006 Chin. Phys. 15 0045
[36] [36]Ma S H, Fang J P, Ren Q B 2007 Acta Phys. Sin. 56 6784 (in Chinese)[马松华、方建平 2007 物理学报 56 6784]
[37] [37]Ma Z Y, Hu Y H 2007 Chaos, Solitons Fractals 34 1667
[38] [38]Wang M L, Li X Z,Zhang J L 2008 Phys. Lett. A 372 417
[39] [39]Zhang S, Tong J L, Wang W 2008 Phys. Lett. A 372 2254
[40] [40]Bekir A. 2008 Phys. Lett. A 372 3400
[41] [41]Zhang J, Wei X L, Lu Y J 2008 Phys. Lett. A 372 3653
[42] [42]Li B Q, Ma Y L 2009 Acta Phys. Sin. 58 4373 (in Chinese)[李帮庆、马玉兰 2009 物理学报58 4373]
[43] [43]Ma Y L, Li B Q, Sun J Z 2009 Acta Phys. Sin. 58 7402 (in Chinese, in press)[ 马玉兰、李帮庆、孙践知 2009 物理学报 58 7402]
[44] [44]Boiti P, Leon J J, Manna M, Pempinelli F 1987 Inverse Problems 3 25
[45] [45]Zeng X, Zhang H Q 2005 Acta Phys. Sin. 54 504 (in Chinese)[曾昕、张鸿庆 2005 物理学报 54 504]
[46] [46]Naranmandula 2002 Acta Phys. Sin. 51 1671 (in Chinese)[那仁满都拉 2009 物理学报 51 1671]
[47] [47]Liu C S 2005 Chin. Phys. 14 1710
[48] [48]Zhang W L, Wu G J, Zhang M, Wang J M, Han J H 2008 Chin. Phys. B 17 1156
-
[1] [1]Wang M L 1995 Phys. Lett. A 199 169
[2] [2]Yan Z Y, Zhang H Q 2000 Acta Phys. Sin. 49 2113 (in Chinese)[闫振亚、张鸿庆 2000 物理学报 49 2113]
[3] [3]Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese)[范恩贵2000 物理学报 49 1409]
[4] [4]Liu S K, Liu S D, Fu Z T 2001 Acta Phys. Sin. 50 2068 (in Chinese)[刘式适、刘适达、付遵涛 2001 物理学报 50 2068]
[5] [5]Liu S D, Fu Z T, Liu S K, Zhao Q 2002 Acta Phys. Sin. 51 718 (in Chinese)[刘式达、付遵涛、刘适式、赵强 2002 物理学报 51 718 ]
[6] [6]Wu G J, Han J H, Shi L M, Zhang M 2006 Acta Phys. Sin. 55 3858 (in Chinese)[吴国将、韩家骅、史良马、张苗 2006 物理学报 55 3858 ]
[7] [7]Wang M L, Zhou Y B, Li Z B 2003 Phys. Lett. A 318 84
[8] [8]Zhou Y B, Wang ML, Miao T D 2004 Phys. Lett. A 323 77
[9] [9]Zhang J L,Wang Y M,Wang M L 2003 Acta Phys. Sin. 52 1574 (in Chinese)[张金良、王跃明、王明亮 2003物理学报 52 1574]
[10] [10]Li X Z, Zhang J L, Wang Y M, Wang M L 2004 Acta Phys. Sin. 53 4045 (in Chinese)[李向正、张金良、王跃明、王明亮 2004 物理学报 53 4045]
[11] [11]Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 13 (in Chinese)[套格图桑、斯仁道尔吉 2006 物理学报 55 13]
[12] [12]Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese)[套格图桑、斯仁道尔吉 2006 物理学报 55 3246]
[13] [13]Li X Z, Li X Y, Zhao L Y, Zhang J L 2008 Acta Phys. Sin. 57 2203 (in Chinese)[李向正、李修勇、赵丽英、张金良 2008 物理学报 57 2203]
[14] [14]Ma Y L, Li B Q 2009 Appl. Math. Comput. 211 102
[15] [15]Lou S Y, Qu C Z, Zhang S L 2006 Chin. Phys. 15 2765
[16] [16]Tang X Y, Liang Z F 2006 Phys. Lett. A 351 398
[17] [17]Zhang S L, Lou S Y, Qu C Z 2006 Chin. Phys. 15 2765
[18] [18]Ma H C, Ge D J, Yu Y D 2008 Chin. Phys. B 17 1448
[19] [19]Ying J P, Lou S Y 2003 Chin. Phys. Lett. 20 1448
[20] [20]Fang J P, Zheng C L, Zhu J M 2005 Commun. Theor. Phys. 44 203
[21] [21]Fang J P, Zheng C L 2005 Chin. Phys. 14 670
[22] [22]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 物理学报 54 2990]
[23] [23]Ma S H, Wu X H, Fang J P, Zheng C L 2006 Z. Naturforsch. 61a 249
[24] [24]Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese)[马松华、方建平 2006 物理学报 55 5611]
[25] [25]Ma S H, Fang J P, Zheng C L 2008 Chin. Phys. B 17 2767
[26] [26]Ma S H, Fang J P,Hong B H, Zheng C L 2008 Commun. Theor. Phys. 49 1245
[27] [27]Huang L, Sun J A, Dou F Q, Duan W S, Liu X X 2007 Acta Phys. Sin. 56 611 (in Chinese)[黄磊、孙建安、豆福全、段文山 2007 物理学报 56 611]
[28] [28]Ma S H, Fang J P, Zheng C L 2007 Z. Naturforsch. 62a 8
[29] [29]Ma S H, Fang J P, Zheng C L 2008 Z. Naturforsch. 63a 121
[30] [30]Li J B, Zheng C L, Ma S H 2008 Z. Naturforsch. 63a 641
[31] [31]Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 0011 (in Chinese)[马松华、吴小红、方建平、郑春龙 2008 物理学报 57 0011]
[32] [32]Lou S Y, Tang X Y 2006 Methods of Nonlinear Mathematical Physics(Beijing: Science Press) p120(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120页]
[33] [33]Ma Z Y, Zhu J M, Zheng C L 2004 Chin. Phys. 13 1382
[34] [34]Zhu J M, Ma Z Y, Zheng C L 2004 Acta Phys. Sin. 53 3248 (in Chinese)[朱加民、马正义、郑春龙 2004 物理学报 53 3248]
[35] [35] Ma Z Y, Zheng C L 2006 Chin. Phys. 15 0045
[36] [36]Ma S H, Fang J P, Ren Q B 2007 Acta Phys. Sin. 56 6784 (in Chinese)[马松华、方建平 2007 物理学报 56 6784]
[37] [37]Ma Z Y, Hu Y H 2007 Chaos, Solitons Fractals 34 1667
[38] [38]Wang M L, Li X Z,Zhang J L 2008 Phys. Lett. A 372 417
[39] [39]Zhang S, Tong J L, Wang W 2008 Phys. Lett. A 372 2254
[40] [40]Bekir A. 2008 Phys. Lett. A 372 3400
[41] [41]Zhang J, Wei X L, Lu Y J 2008 Phys. Lett. A 372 3653
[42] [42]Li B Q, Ma Y L 2009 Acta Phys. Sin. 58 4373 (in Chinese)[李帮庆、马玉兰 2009 物理学报58 4373]
[43] [43]Ma Y L, Li B Q, Sun J Z 2009 Acta Phys. Sin. 58 7402 (in Chinese, in press)[ 马玉兰、李帮庆、孙践知 2009 物理学报 58 7402]
[44] [44]Boiti P, Leon J J, Manna M, Pempinelli F 1987 Inverse Problems 3 25
[45] [45]Zeng X, Zhang H Q 2005 Acta Phys. Sin. 54 504 (in Chinese)[曾昕、张鸿庆 2005 物理学报 54 504]
[46] [46]Naranmandula 2002 Acta Phys. Sin. 51 1671 (in Chinese)[那仁满都拉 2009 物理学报 51 1671]
[47] [47]Liu C S 2005 Chin. Phys. 14 1710
[48] [48]Zhang W L, Wu G J, Zhang M, Wang J M, Han J H 2008 Chin. Phys. B 17 1156
计量
- 文章访问数: 9019
- PDF下载量: 1514
- 被引次数: 0