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## 留言板

(2+1)维广义Calogero-Bogoyavlenskii-Schiff方程的无穷序列类孤子解

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## New infinite sequence soliton-like solutions of (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Taogetusang
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• #### 摘要

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.

#### Abstract

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.

#### 作者及机构信息

###### 1. 内蒙古师范大学数学科学学院, 呼和浩特 010022
• 基金项目: 国家自然科学基金(批准号: 11361040)、内蒙古自治区高等学校科学研究基金(批准号: NJZY12031)和内蒙古自治区自然科学基金(批准号: 2010MS0111)资助的课题.

#### Authors and contacts

###### 1. The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China
• Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11361040), the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZY12031), and the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2010MS0111).

#### 参考文献

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#### 施引文献

•  [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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 58 7393] [29] Bogoyavlenskii O I 1990 Math. USSR. Izv. 34 247
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##### 出版历程
• 收稿日期:  2013-06-13
• 修回日期:  2013-08-05
• 刊出日期:  2013-11-05

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