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给出椭圆方程的一组Riemann 函数解, 结合它的一个Backlund变换, 得到这个椭圆方程的无穷序列Riemann 函数解. 最后利用这个椭圆方程作为辅助方程, 借助于符号计算软件 Mathematica, 得到了修正的Korteweg de Vries-正弦Gordon方程的无穷序列Riemann 函数解.Based on some Riemnan theta function solutions to a elliptical equation, together with its Backlund transformation, infinite sequences Riemann function solutions are derived, then regarding this elliptical equation as an auxiliary equation, with the help of computer software (Mathematica), infinite sequences Riemann function solutions to the modified Korteweg de Vries sine-Gordon equation are obtained.
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Keywords:
- modified Korteweg de Vries-sine-Gordon equation /
- Backlund transformation /
- Riemann function solutions
[1] Gardner C S, Greene J M, Kruskal M D, Miura R M 1967 Phys. Rev. Lett. 19 1095
[2] Gardner C S, Greene J M, Kruskal M D, Miura R M 1974 Commun. Pure Appl. Math. 27 97
[3] Cao C W, Wu Y T, Geng X G 1999 J. Math. Phys. 40 3948
[4] Cao C W, Geng X G, Wu Y T 1999 J. Phys. A 32 8059
[5] Wang M L 1995 Phys. Lett. A 199 169
[6] Parkes E J, Duffy B R 1996 Comput. Phys. Commun. 98 288
[7] Fan E G 2000 Phys. Lett. A 277 212
[8] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese) [范恩贵, 张鸿庆 1998 物理学报 47 353]
[9] Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese) [范恩贵 2000 物理学报 49 1409]
[10] Shi Y R, Lü K P, Duan W S, Hong X R, Zhao J B 2003 Acta Phys. Sin. 52 267 (in Chinese) [石玉仁, 吕克璞, 段文山, 洪学仁, 赵金宝 2003 物理学报 52 267]
[11] Liu S K, Fu Z T, Liu S D, Zhao Q 2001 Acta Phys. Sin. 50 2068 (in Chinese) [刘式适, 傅遵涛, 刘式达, 赵强 2001 物理学报 50 2068]
[12] Zhao S L, Zhang D J, Ji J 2010 Chin. Phys. Lett. 27 020201
[13] Wang J M 2011 Chin. Phys. Lett. 28 030202
[14] Wang J M, Yang X 2011 Chin. Phys. Lett. 28 090202
[15] Wang J M, Ji J 2008 Commun. Theor. Phys. 49 1407
[16] Geng X G, Cao C W 2001 Nonlinearity 14 1433
[17] Nakamura A 1979 J. Phys. Soc. Jpn. 47 1701
[18] Nakamura A 1980 J. Phys. Soc. Jpn. 48 1365
[19] Fan E G, Hon Y C 2008 Phys. Rev. E 78 036607
[20] Ma W X, Zhou R G, Gao L 2009 Mod. Phys. Lett. A 21 1677
[21] Zhao H 2007 Commun. Theor. Phys. 47 1013
[22] Taogetusang 2011 Acta Phys. Sin. 60 070203 (in Chinese) [套格图桑 2011 物理学报 60 070203]
[23] Lawden D F 1989 Elliptic Functions and Applications (Berlin: Springer-Verlag) p496
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[1] Gardner C S, Greene J M, Kruskal M D, Miura R M 1967 Phys. Rev. Lett. 19 1095
[2] Gardner C S, Greene J M, Kruskal M D, Miura R M 1974 Commun. Pure Appl. Math. 27 97
[3] Cao C W, Wu Y T, Geng X G 1999 J. Math. Phys. 40 3948
[4] Cao C W, Geng X G, Wu Y T 1999 J. Phys. A 32 8059
[5] Wang M L 1995 Phys. Lett. A 199 169
[6] Parkes E J, Duffy B R 1996 Comput. Phys. Commun. 98 288
[7] Fan E G 2000 Phys. Lett. A 277 212
[8] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese) [范恩贵, 张鸿庆 1998 物理学报 47 353]
[9] Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese) [范恩贵 2000 物理学报 49 1409]
[10] Shi Y R, Lü K P, Duan W S, Hong X R, Zhao J B 2003 Acta Phys. Sin. 52 267 (in Chinese) [石玉仁, 吕克璞, 段文山, 洪学仁, 赵金宝 2003 物理学报 52 267]
[11] Liu S K, Fu Z T, Liu S D, Zhao Q 2001 Acta Phys. Sin. 50 2068 (in Chinese) [刘式适, 傅遵涛, 刘式达, 赵强 2001 物理学报 50 2068]
[12] Zhao S L, Zhang D J, Ji J 2010 Chin. Phys. Lett. 27 020201
[13] Wang J M 2011 Chin. Phys. Lett. 28 030202
[14] Wang J M, Yang X 2011 Chin. Phys. Lett. 28 090202
[15] Wang J M, Ji J 2008 Commun. Theor. Phys. 49 1407
[16] Geng X G, Cao C W 2001 Nonlinearity 14 1433
[17] Nakamura A 1979 J. Phys. Soc. Jpn. 47 1701
[18] Nakamura A 1980 J. Phys. Soc. Jpn. 48 1365
[19] Fan E G, Hon Y C 2008 Phys. Rev. E 78 036607
[20] Ma W X, Zhou R G, Gao L 2009 Mod. Phys. Lett. A 21 1677
[21] Zhao H 2007 Commun. Theor. Phys. 47 1013
[22] Taogetusang 2011 Acta Phys. Sin. 60 070203 (in Chinese) [套格图桑 2011 物理学报 60 070203]
[23] Lawden D F 1989 Elliptic Functions and Applications (Berlin: Springer-Verlag) p496
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