In the present paper, we consider a special class of third-order polynomial evolutionary equations. These equations, via Lie theory admit the same one-parameter point transformations which leave the equations invariant. Reductions with these invariant functions lead to highly nonlinear third-order ordinary differential equations. We use a power series to establish interesting solutions to the reduced equations, whereby recurrence relations occur and convergence of the series may be tested. Finally, the conserved vectors of the class are constructed.

中文翻译：

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一类三阶多项式演化方程的守恒定律、李对称性分析及幂级数解

在本文中，我们考虑了一类特殊的三阶多项式进化方程。这些方程，通过李理论，允许相同的单参数点变换，使方程保持不变。使用这些不变函数进行归约会得到高度非线性的三阶常微分方程。我们使用幂级数为简化方程建立有趣的解，从而出现递归关系并且可以检验级数的收敛性。最后，构造该类的保守向量。