Similarity Reductions for a Generalized Variable-Coefficient Kadomtsev-Petviashvili Equation with Symbolic Computation
Similarity Reductions for a Generalized Variable-Coefficient Kadomtsev-Petviashvili Equation with Symbolic Computation
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DOI：
10.1142/s0129183199000899
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发表时间：
1999-09
影响因子：
1.9
通讯作者：
B. Tian
中科院分区：
文献类型：
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作者：
B. Tian
我们使用计算机符号计算来研究广义Kadomtsev-Petviashvili （KP）方程的相似性约简，其空间和时间依赖系数出现在等离子体物理学和流体力学中。我们得到了涉及这些系数函数的几个约简，其中一个是对第四painlevel方程的约简，而另一个是对第二painlevel方程、第一painlevel方程或weerstrass椭圆函数方程的约简。我们的结果与Painleve猜想一致。以柱面KP方程为例，描述了浅水中具有弱方位依赖性的非线性柱面水波。
We use computerized symbolic computation to study the similarity reductions of a generalized Kadomtsev–Petviashvili (KP) equation, with its space- and time-dependent coefficients arising in plasma physics and fluid mechanics. We obtain a couple of reductions involving those coefficient functions, one of which is to the fourth Painleve equation, while the other is to one of the second Painleve equation, the first Painleve equation or a Weierstrass elliptic function equation. Our results agree with the Painleve Conjecture. The cylindrical KP equation is presented as an example, which describes nonlinear cylindrical water waves in shallow water with a weak azimuthal dependence.