We consider a nonlinear Sobolev equation of the third order describing the electric field potential in a conductor. Six classes of exact solutions are constructed, and their qualitative behavior is analyzed.

中文翻译：

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非线性导体模型方程的精确解

我们考虑描述导体中电场势的三阶非线性 Sobolev 方程。构造了六类精确解，并分析了它们的定性行为。