Nonlinear PDE’s having given conditional symmetries are constructed. They are obtained starting from the invariants of the conditional symmetry generator and imposing the extra condition given by the characteristic of the symmetry. Series of examples starting from the Boussinesq and including non-autonomous Korteweg–de Vries like equations are given to show and clarify the methodology introduced.

中文翻译：

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条件对称下不变量的微分方程

构造了具有给定条件对称性的非线性偏微分方程。它们是从条件对称生成器的不变量开始并施加由对称特性给出的额外条件获得的。给出了一系列从 Boussinesq 开始的例子，包括非自治的 Korteweg-de Vries 等方程，以展示和阐明所引入的方法。