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为了构造非线性发展方程的无穷序列复合型类孤子新解, 进一步研究了G'(ξ)/G(ξ) 展开法. 首先, 给出一种函数变换, 把常系数二阶齐次线性常微分方程的求解问题转化为一元二次方程和Riccati方程的求解问题. 然后, 利用Riccati方程解的非线性叠加公式, 获得了常系数二阶齐次线性常微分方程的无穷序列复合型新解. 在此基础上, 借助符号计算系统Mathematica, 构造了改进的(2+1)维色散水波系统和(2+1)维色散长波方程的无穷序列复合型类孤子新精确解.
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关键词:
- G'(ξ)/G(ξ)展开法 /
- 非线性叠加公式 /
- 非线性发展方程 /
- 复合型类孤子新解
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.-
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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