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

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套格图桑. 2013: （2+1）维广义Calogero-Bogoyavlenskii-Schiff方程的无穷序列类孤子解, 物理学报, null(21): 12-18. doi: 10.7498/aps.62.210201
引用本文: 套格图桑. 2013: （2+1）维广义Calogero-Bogoyavlenskii-Schiff方程的无穷序列类孤子解, 物理学报, null(21): 12-18. doi: 10.7498/aps.62.210201
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Taogetusang. 2013: New infinite sequence soliton-like solutions of (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation, Acta Physica Sinica, null(21): 12-18. doi: 10.7498/aps.62.210201
Citation: Taogetusang. 2013: New infinite sequence soliton-like solutions of (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation, Acta Physica Sinica, null(21): 12-18. doi: 10.7498/aps.62.210201
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（2+1）维广义Calogero-Bogoyavlenskii-Schiff方程的无穷序列类孤子解

  • 内蒙古师范大学数学科学学院,呼和浩特,010022

    • 通讯作者: 套格图桑

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

    Corresponding author: Taogetusang

  • 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 ho-mogeneous 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 gener-alized Calogero-Bogoyavlenskii-Schiff equation are constructed using the above conclusion and the symbolic computation system Mathematica.
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  • 刊出日期:  2013-11-15

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

    通讯作者: 套格图桑
  • 内蒙古师范大学数学科学学院,呼和浩特,010022

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。

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