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| 一般变系数KdV方程的自-BT和变速孤立波解 | |
| 引用本文： | 张金良,王跃明,王明亮,李琦.一般变系数KdV方程的自-BT和变速孤立波解[J].河南科技大学学报(自然科学版),2000,21(3). |
| 作者姓名： | 张金良 王跃明 王明亮 李琦 |
| 作者单位： | 1. 洛阳工学院,应用数学系,河南,洛阳,471039 2. 洛阳工学院,应用数学系,河南,洛阳,471039;兰州大学,数学系,甘肃,兰州,730000 3. 四川教育学院,数学系,四川,成都,610041 |
| 基金项目： | 甘肃省自然科学基金!(ZR -97-0 0 2 )，洛阳工学院科学研究基金!(9910 )资助项目 |
| 摘 要： | 设方程的系数满足线性相关条件 ,用齐次平衡原则导出了一般变系数KdV方程的自—Backlund变换(BT)。利用BT获得了变系数KdV方程的变速孤立波解 ,方程的系数不改变孤立波的波形 ,但是直接改变孤立波的传播速度 ,对于孤立波的振幅影响是增大或减小常数倍 ,该常数正是方程的变系数之间的一比例常数。 |
| 关 键 词： | 变系数KdV方程 齐次平衡原则 自—BT 变速孤立波解 |
Anto-Backland Transformation and Solitary Wave Solution with Variable Velocity to the KdV Equation with Variable Coefficients |
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| ZHANG Jin-Liang,WANG Yue-Ming,WANG Ming-Liang,Li Qi.Anto-Backland Transformation and Solitary Wave Solution with Variable Velocity to the KdV Equation with Variable Coefficients[J].Journal of Henan University of Science & Technology:Natural Science,2000,21(3). | |
| Authors: | ZHANG Jin-Liang WANG Yue-Ming WANG Ming-Liang Li Qi |
| Abstract: | By using the homogeneous balance principle, an auto Backland Transformation (BT) to the KdV equation with variable coefficients is derived if the coefficients of the equation are linearly dependent. In terms of the BT, a solitary wave solution with variable propagation velocity is obtained. The variable coefficients directly change the propagation velocity of the solitary wave, and the vibration amplitude effected of the solitary wave will be increased or decreased in a constant times.This constant is just a proportional costant among these variable coefficients of the equation. |
| Keywords: | KdV equation with variable coefficients Homogeneous balance principle Auto-BT Solitary wave solution with variable velocity |
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