On singularity of a nonlinear variational sine-Gordon equation
On singularity of a nonlinear variational sine-Gordon equation
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DOI：
10.1016/s0022-0396(02)00150-x
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发表时间：
2003-03
影响因子：
2.4
通讯作者：
Kyungwoo Song
中科院分区：
文献类型：
--
作者：
Kyungwoo Song
研究了一个sine-Gordon型非线性变分波动方程，其波速是振幅的正弦函数。这个方程自然地产生于连续极限中偶极链上的长波，这为某些聚合物提供了一个粗略的模型。利用特征线方法，我们描述了一维非线性变分sine-Gordon方程的爆破结果，表明光滑解在有限时间内破裂。
We study a sine-Gordon-type of nonlinear variational wave equation whose wave speed is a sinusoidal function of the wave amplitude. This equation arises naturally from long waves on a dipole chain in the continuum limit, which provides a crude model for some polymers. Using characteristic methods, we describe a blow-up result for the one-dimensional nonlinear variational sine-Gordon equation, which shows that smooth solutions breakdown in finite time.