Similarity solutions of dispersive long‐wave equations in two space dimensions
Similarity solutions of dispersive long‐wave equations in two space dimensions
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DOI：
10.1002/mma.1670181004
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发表时间：
1995-08
影响因子：
2.9
通讯作者：
Lou Sen-yue
中科院分区：
文献类型：
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作者：
Lou Sen-yue
本文采用直接方法和非经典Lie方法对(2+1)维色散长波方程进行了降阶。给出了9种二维PDE约化和13种常微分方程组约化。将经典Lie方法得到的所有已知约化结果作为特例重新得到。类似于(1+1)维的情形，尽管模型是可积的，但允许某些类型的具有本质和对数奇异特征流形的约简。
In this paper, both the direct method and the non-classical Lie approach are applied to reduce the (2 + 1)-dimensional dispersive long wave equations. Nine types of two-dimensional PDE reductions and 13 types of ODE reductions are given. All the known reductions obtained by the classical Lie approach are reobtained as some special cases. Similar to the (1 + 1)-dimensional case, some types of reductions with essential and logarithmic singular characteristic manifolds are allowed although the model is integrable.