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The G'(ξ)/G(ξ) expansion method is further studied for constructing new infinite sequence complexion soliton-like solutions of nonlinear evolution equations. First, to solve a linear ordinary differential equation with constant coefficients of second order is changed into the solving of one unknown quadratic equation and Riccati equation by a function transformation. Then a nonlinear superposition formula of the solutions to Riccati equation is presented to seek new infinite sequence complexion solutions of a second order linear ordinary differential equation with constant coefficients. Based on this, the new infinite sequence complexion soliton-like solutions to (2+1)-dimensional modified dispersive water wave system and (2+1)-dimensional dispersive long-wave equation are obtained with the help of symbolic computation system Mathematica.
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Keywords:
- the G'(ξ)/G(ξ) expansion method /
- nonlinear superposition formula /
- nonlinear evolution equation /
- new complexion soliton-like solution
[1] Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[2] Ma S H, Fang J P 2012 Acta. Phys. Sin. 61 180505 (in Chinese) [马松华, 方建平 2012 61 180505]
[3] Ma Z Y, Ma S H, Yang Y 2012 Acta. Phys. Sin. 61 190508 (in Chinese) [马正义, 马松华, 杨毅 2012 61 190508]
[4] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[5] Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[6] L Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[7] Ma S H, Fang J P, Zhu H P 2007 Acta. Phys. Sin. 56 4319 (in Chinese) [马松华, 方建平, 朱海平 2007 56 4319]
[8] Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[9] Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[10] Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[11] Ma Y L, Li B Q, Sun J Z 2009 Acta. Phys. Sin. 58 7403 (in Chinese) [马玉兰, 李帮庆, 孙践知 2009 58 7403]
[12] Li B Q, Ma Y L, Xu M P 2010 Acta. Phys. Sin. 59 1409 (in Chinese) [李帮庆, 马玉兰 ,徐美萍 2010 59 1409]
[13] Li B Q, Ma Y L 2009 Acta. Phys. Sin. 58 4373 (in Chinese) [李帮庆, 马玉兰 2009 58 4373]
[14] Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A372 417
[15] Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. (Beijing) 55 949
[16] Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. B 19 080303
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[1] Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[2] Ma S H, Fang J P 2012 Acta. Phys. Sin. 61 180505 (in Chinese) [马松华, 方建平 2012 61 180505]
[3] Ma Z Y, Ma S H, Yang Y 2012 Acta. Phys. Sin. 61 190508 (in Chinese) [马正义, 马松华, 杨毅 2012 61 190508]
[4] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[5] Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[6] L Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[7] Ma S H, Fang J P, Zhu H P 2007 Acta. Phys. Sin. 56 4319 (in Chinese) [马松华, 方建平, 朱海平 2007 56 4319]
[8] Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[9] Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[10] Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[11] Ma Y L, Li B Q, Sun J Z 2009 Acta. Phys. Sin. 58 7403 (in Chinese) [马玉兰, 李帮庆, 孙践知 2009 58 7403]
[12] Li B Q, Ma Y L, Xu M P 2010 Acta. Phys. Sin. 59 1409 (in Chinese) [李帮庆, 马玉兰 ,徐美萍 2010 59 1409]
[13] Li B Q, Ma Y L 2009 Acta. Phys. Sin. 58 4373 (in Chinese) [李帮庆, 马玉兰 2009 58 4373]
[14] Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A372 417
[15] Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. (Beijing) 55 949
[16] Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. B 19 080303
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