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为了构造高维非线性发展方程的无穷序列类孤子新解, 研究了二阶常系数齐次线性常微分方程, 获得了新结论. 步骤一, 给出一种函数变换把二阶常系数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. 在此基础上, 利用Riccati方程解的非线性叠加公式, 获得了二阶常系数齐次线性常微分方程的无穷序列新解. 步骤二, 利用以上得到的结论与符号计算系统Mathematica, 构造了(2+1)维广义Calogero-Bogoyavlenskii-Schiff (GCBS)方程的无穷序列类孤子新解.This paper will study in detail homogeneous linear ordinary differential equation with constant coefficients of second order and draw new conclusion to construct new infinite sequence soliton-like solutions of high-dimensional nonlinear evolution equations. Step one: the solving of a homogeneous linear ordinary differential equation with constant coefficients of second order is changed into the solving of the quadratic equation with one unknown and the Riccati equation. Based on this, new infinite sequence solutions of homogeneous linear ordinary differential equation with constant coefficients of second order are found by using nonlinear superposition formula for the solutions to Riccati equation. Step two: new infinite sequence soliton-like solutions to (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation are constructed using the above conclusion and the symbolic computation system Mathematica.
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Keywords:
- ordinary differential equation /
- the nonlinear superposition formula /
- high-dimensional nonlinear evolution equation /
- infinite sequence soliton-like solution
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[2] Tang X Y, Liang Z F 2006 Phys. Lett. A 351 398
[3] Ying J P, Lou S Y 2003 Chin. Phys. Lett. 20 1448
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[19] Mustafa Inca, Esma Ulutas, Anjan Biswasc 2013 Chin. Phys. B 22 060204
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[21] Khaled A Gepreel, Saleh Omran 2012 Chin. Phys. B 21 110204
[22] Zhang S 2007 Phys. Lett. A 368 470
[23] Pan Z H, Ma S H, Fang J P 2010 Chin. Phys. B 19 100301
[24] Ma S H, Fang J P, Zheng C L 2008 Chin. Phys. B 17 2767
[25] Shi L F, Chen C S, Zhou X C 2011 Chin. Phys. B 20 100507
[26] Qiang J Y, Ma S H, Fang J P 2010 Chin. Phys. B 19 090305
[27] Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. 19 080303
[28] Zhang H P, Chen Y, Li B 2009 Acta. Phys. Sin. 58 7393 (in Chinese) [张焕萍, 陈勇, 李彪 2003 58 7393]
[29] Bogoyavlenskii O I 1990 Math. USSR. Izv. 34 247
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[1] Lou S Y 2000 Phys. Lett. A 277 94
[2] Tang X Y, Liang Z F 2006 Phys. Lett. A 351 398
[3] Ying J P, Lou S Y 2003 Chin. Phys. Lett. 20 1448
[4] Ma S H, Fang J P 2012 Acta. Phys. Sin. 61 180505 (in Chinese) [马松华, 方建平 2012 61 180505]
[5] Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[6] Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[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] 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]
[9] Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[10] Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[11] Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[12] L Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[13] Xie F D, Gao X S 2004 Commun. Theor. Phys. (Beijing) 41 353
[14] Chen Y, Li B 2004 Commun. Theor. Phys. (Beijing) 41 1
[15] Li B Q, Ma Y L 2009 Acta. Phys. Sin. 58 4373 (in Chinese) [李帮庆, 马玉兰 2009 58 4373]
[16] 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]
[17] 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]
[18] Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A372 417
[19] Mustafa Inca, Esma Ulutas, Anjan Biswasc 2013 Chin. Phys. B 22 060204
[20] Sirendaoreji, Sun J 2003 Phys. Lett. A309 387
[21] Khaled A Gepreel, Saleh Omran 2012 Chin. Phys. B 21 110204
[22] Zhang S 2007 Phys. Lett. A 368 470
[23] Pan Z H, Ma S H, Fang J P 2010 Chin. Phys. B 19 100301
[24] Ma S H, Fang J P, Zheng C L 2008 Chin. Phys. B 17 2767
[25] Shi L F, Chen C S, Zhou X C 2011 Chin. Phys. B 20 100507
[26] Qiang J Y, Ma S H, Fang J P 2010 Chin. Phys. B 19 090305
[27] Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. 19 080303
[28] Zhang H P, Chen Y, Li B 2009 Acta. Phys. Sin. 58 7393 (in Chinese) [张焕萍, 陈勇, 李彪 2003 58 7393]
[29] Bogoyavlenskii O I 1990 Math. USSR. Izv. 34 247
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