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给出包含第一种椭圆方程的三角函数型辅助方程及其解的叠加公式.在一般函数变换下,借助符号计算系统Mathematica,构造了(n+1)维双sine-Gordon方程新的Jacobi椭圆函数精确解.这些解包括了行波变换下的Jacobi椭圆函数精确解、精确孤立波解和三角函数解.
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关键词:
- 解的叠加公式 /
- (n+1)维双sine-Gordon方程 /
- 三角函数型辅助方程 /
- Jacobi椭圆函数
The auxiliary equation of triangular function type including the first kind of elliptic equation and the formula of superposition of the solutions are given. Then based on general function transformation, new Jacobi elliptic exact solutions to (n+1)-dimensional double sine-Gordon equation are constructed with aid of symbolic computation system Mathematica. And the solutions include Jacobi elliptic function exact solutions, exact solitary wave solutions and triangular functions.-
Keywords:
- the formula of superposition of solutions /
- (n+1)-dimensional double sine-Gordon equation /
- auxiliary equation of triangular type /
- Jacobi elliptic function
[1] Wang M L 1995 Phys.Lett. A 199 169
[2] Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta.Phys.Sin. 51 1923(in Chinese)[刘式适、付遵涛、刘式达、赵 强 2002 51 1923]
[3] Yan Z Y, Zhang H Q 1999 Acta.Phys.Sin.48 1957(in Chinese) [闫振亚、张鸿庆 1999 48 1957]
[4] Lu D C, Hong B J, Tian L X 2006 Acta.Phys.Sin.55 5617(in Chinese)[卢殿臣、烘宝剑、田立新2006 55 5617]
[5] Sirendaoreji, Sun J 2003 Phys.Lett.A 309 387
[6] Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin. Phys. 12 825
[7] Fan E G 2000 Phys.Lett. A 277 212
[8] Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 1569 (in Chinese)[李德生、张鸿庆 2003 52 1569]
[9] Li H M 2005 Chin.Phys. 14 251
[10] Yang X L, Tang J S 2008 Acta.Phys.Sin. 57 3305(in Chinese)[杨先林、唐驾时 2008 57 3305]
[11] Zhao X Q, Zhi H Y, Zhang H Q 2006 Chin.Phys. 15 2202
[12] Liu G T, Fan T Y 2004 Acta.Phys.Sin. 53 676(in Chinese) [刘官厅、范天佑 2004 53 676]
[13] Han Z X 2005 Acta.Phys.Sin. 54 1481(in Chinese)[韩兆秀 2005 54 1481]
[14] Sirendaoreji, Sun J 2002 Phys.Lett. A 298 133
[15] Xie Y X, Tang J S 2005 Chin.Phys. 14 1303
[16] Taogetusang, Sirendaoreji 2004 Acta Sci.J.Nat.Univ.Nei Mongol 33 361(in Chinese)[套格图桑、斯仁道尔吉 2004 内蒙古师范大学学报 33 361]
[17] Li J B 2007 Sci. China. Series. A Math. 50 153
[18] Wazwaz A M 2006 Phys.Lett.A 350 367
[19] Zhou J P, Yan Z L 2007 Chinese Journal of Quantum Electronics 24 535(in Chinese)[周建平、闫志莲 2007量子电子学报 24 535]
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[1] Wang M L 1995 Phys.Lett. A 199 169
[2] Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta.Phys.Sin. 51 1923(in Chinese)[刘式适、付遵涛、刘式达、赵 强 2002 51 1923]
[3] Yan Z Y, Zhang H Q 1999 Acta.Phys.Sin.48 1957(in Chinese) [闫振亚、张鸿庆 1999 48 1957]
[4] Lu D C, Hong B J, Tian L X 2006 Acta.Phys.Sin.55 5617(in Chinese)[卢殿臣、烘宝剑、田立新2006 55 5617]
[5] Sirendaoreji, Sun J 2003 Phys.Lett.A 309 387
[6] Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin. Phys. 12 825
[7] Fan E G 2000 Phys.Lett. A 277 212
[8] Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 1569 (in Chinese)[李德生、张鸿庆 2003 52 1569]
[9] Li H M 2005 Chin.Phys. 14 251
[10] Yang X L, Tang J S 2008 Acta.Phys.Sin. 57 3305(in Chinese)[杨先林、唐驾时 2008 57 3305]
[11] Zhao X Q, Zhi H Y, Zhang H Q 2006 Chin.Phys. 15 2202
[12] Liu G T, Fan T Y 2004 Acta.Phys.Sin. 53 676(in Chinese) [刘官厅、范天佑 2004 53 676]
[13] Han Z X 2005 Acta.Phys.Sin. 54 1481(in Chinese)[韩兆秀 2005 54 1481]
[14] Sirendaoreji, Sun J 2002 Phys.Lett. A 298 133
[15] Xie Y X, Tang J S 2005 Chin.Phys. 14 1303
[16] Taogetusang, Sirendaoreji 2004 Acta Sci.J.Nat.Univ.Nei Mongol 33 361(in Chinese)[套格图桑、斯仁道尔吉 2004 内蒙古师范大学学报 33 361]
[17] Li J B 2007 Sci. China. Series. A Math. 50 153
[18] Wazwaz A M 2006 Phys.Lett.A 350 367
[19] Zhou J P, Yan Z L 2007 Chinese Journal of Quantum Electronics 24 535(in Chinese)[周建平、闫志莲 2007量子电子学报 24 535]
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