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To seek infinite sequence exact solutions to nonlinear difference-differential equations, a kind of auxiliary equation of hyperbolic function type is intruduced, and the Bä,cklund transformation of the solutions to the equation and the formula of nonlinear supperposition of solutions are presented. Based on these and combing auxiliary equation with function transformation, the general lattice equation is chosen as example for which the infinite sequence exact solutionsto the equation are obtained.
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Keywords:
- nonlinear difference-differential equation /
- function transformation /
- auxiliary equation of hyperbolic function type /
- infinite sequence exact solution
[1] Wang M L 1995 Phys. Lett. A 199 169
[2] Parkes E J, Duffy B R 1996 Comput. Phys. Commun. 98 288
[3] Fan E G 2000 Phys.Lett. A 277 212
[4] Li H M 2005 Chin.Phys. 14 251
[5] Sirendaoerji, Sun J 2003 Phys.Lett. A 309 387
[6] Taogetusang, Sirendaoerji 2006 Acta Phys.Sin. 55 3246(in Chinese)[套格图桑、斯仁道尔吉 2006 55 3246]
[7] Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin. Phys. 12 825
[8] Lu B, Zhang H Q 2008 Chin. Phys. B 17 3974
[9] Li H M 2005 Chin. Phys. 14 251
[10] Xie F D, Gao X S 2003 Commun. Theor. Phys. 41 353
[11] Chen Y, Li B 2004 Commun. Theor. Phys. 41 1
[12] Yong X L, Zhang H Q 2005 Acta Phys. Sin. 54 2514(inChinese)[雍雪林、张鸿庆 2005 54 1514]
[13] 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]
[14] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. 42 497
[15] Xie F D, Yuan Z T 2005 Commun. Theor. Phys. 43 39
[16] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11(in Chinese)[马松华、 吴小红、 方建平、 郑春龙 2008 57 11]
[17] Ma S H, Fang J P, Zheng C L 2008 Chin.Phys. B 17 2767
[18] Yang X L, Tang J S 2008 Acta Phys. Sin. 57 3305(in Chinese)[杨先林、唐驾时 2008 57 3305]
[19] Zhu J M, Ma Z Y, Zheng S L 2005 Acta Phys. Sin. 54 483(in Chinese)[朱加民、马正义、郑春龙 2005 54 483]
[20] Yu Y X, Wang Q, Zhao X Q, Zhi H Y, Zhang H Q 2005 Acta Phys. Sin. 54 3992(in Chinese)[于亚璇、 王 琪、 赵雪芹、 智红燕、张鸿庆 2005 54 3992]
[21] Zhu J M 2005 Chin. Phys. 14 1290
[22] Zhu J M, Ma Z Y 2005 Chin. Phys. 14 17
[23] Zha Q L , Sirendaoerji 2006 Chin. Phys. 15 475
[24] Wang Z, Zhang H Q 2006 Chin. Phys. 15 2210
[25] Zhang S Q 2007 Acta Phys.Sin. 56 1870(in Chinese)[张善卿 2007 56 1870]
[26] Taogetusang, Sirendaoerji 2009 Acta Phys.Sin. 58 5887(in Chinese)[套格图桑、斯仁道尔吉 2009 58 5887]
[27] Taogetusang, Sirendaoerji 2009 Acta Phys.Sin. 58 5894(in Chinese)[套格图桑、斯仁道尔吉 2009 58 5894]
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[1] Wang M L 1995 Phys. Lett. A 199 169
[2] Parkes E J, Duffy B R 1996 Comput. Phys. Commun. 98 288
[3] Fan E G 2000 Phys.Lett. A 277 212
[4] Li H M 2005 Chin.Phys. 14 251
[5] Sirendaoerji, Sun J 2003 Phys.Lett. A 309 387
[6] Taogetusang, Sirendaoerji 2006 Acta Phys.Sin. 55 3246(in Chinese)[套格图桑、斯仁道尔吉 2006 55 3246]
[7] Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin. Phys. 12 825
[8] Lu B, Zhang H Q 2008 Chin. Phys. B 17 3974
[9] Li H M 2005 Chin. Phys. 14 251
[10] Xie F D, Gao X S 2003 Commun. Theor. Phys. 41 353
[11] Chen Y, Li B 2004 Commun. Theor. Phys. 41 1
[12] Yong X L, Zhang H Q 2005 Acta Phys. Sin. 54 2514(inChinese)[雍雪林、张鸿庆 2005 54 1514]
[13] 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]
[14] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. 42 497
[15] Xie F D, Yuan Z T 2005 Commun. Theor. Phys. 43 39
[16] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11(in Chinese)[马松华、 吴小红、 方建平、 郑春龙 2008 57 11]
[17] Ma S H, Fang J P, Zheng C L 2008 Chin.Phys. B 17 2767
[18] Yang X L, Tang J S 2008 Acta Phys. Sin. 57 3305(in Chinese)[杨先林、唐驾时 2008 57 3305]
[19] Zhu J M, Ma Z Y, Zheng S L 2005 Acta Phys. Sin. 54 483(in Chinese)[朱加民、马正义、郑春龙 2005 54 483]
[20] Yu Y X, Wang Q, Zhao X Q, Zhi H Y, Zhang H Q 2005 Acta Phys. Sin. 54 3992(in Chinese)[于亚璇、 王 琪、 赵雪芹、 智红燕、张鸿庆 2005 54 3992]
[21] Zhu J M 2005 Chin. Phys. 14 1290
[22] Zhu J M, Ma Z Y 2005 Chin. Phys. 14 17
[23] Zha Q L , Sirendaoerji 2006 Chin. Phys. 15 475
[24] Wang Z, Zhang H Q 2006 Chin. Phys. 15 2210
[25] Zhang S Q 2007 Acta Phys.Sin. 56 1870(in Chinese)[张善卿 2007 56 1870]
[26] Taogetusang, Sirendaoerji 2009 Acta Phys.Sin. 58 5887(in Chinese)[套格图桑、斯仁道尔吉 2009 58 5887]
[27] Taogetusang, Sirendaoerji 2009 Acta Phys.Sin. 58 5894(in Chinese)[套格图桑、斯仁道尔吉 2009 58 5894]
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