| 变系数Sine-Gordon方程的反散射变换 |
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| 引用本文： | 徐宝智,赵申琪.变系数Sine-Gordon方程的反散射变换[J].高校应用数学学报(英文版),1994,9(4):331-337. |
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| 作者姓名： | 徐宝智 赵申琪 |
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| 摘 要： | In this paper, the variable coefficient Sine-Gordon type equation uxt=a(t)sinu β(t)uxx k(t)(xux)x is discussed. It is related to the eigenvalue problem Vx=QV.The structure equation and the evolution laws of scattering data for the second equation are derived and the inverse scattering solution of the first equation is obtained.
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| 关 键 词： | 变系数Sine-Gordon方程 反散射变换 偏微分 特征值问题 |
Inverse scattering transformation for the variable coefficient Sine-Gordon type equation |
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| Xu Baozhi,Zhao Shenqi.Inverse scattering transformation for the variable coefficient Sine-Gordon type equation[J].Applied Mathematics A Journal of Chinese Universities,1994,9(4):331-337. |
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| Authors: | Xu Baozhi Zhao Shenqi |
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| Institution: | 1. Department of Applied Mathematics, Zhejiang University, 310027, Hangzhou
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| Abstract: | In this paper, the variable coefficient Sine-Gordon type equation $$u_{xt} = \alpha \left( t \right)\sin u + \beta \left( t \right)u_{xx} + k\left( t \right)\left( {xu_x } \right)_x $$ is discussed. It is related to the eigenvalue problem $$V_x = QV$$ . The structure equation and the evolution laws of scattering data for the second equation are derived and the inverse scattering solution of the first equation is obtained. |
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