A class of PDEs with nonlinear superposition principles. (English) Zbl 1246.35021

Summary: Through assuming that nonlinear superposition principles (NLSPs) are embedded in a Lie group, a class of 3rd-order PDEs is derived from a general determining equation that determines the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the governing PDE is proved to be \(C\)-integrable. In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations to linearization of partial differential equations.


35B06 Symmetries, invariants, etc. in context of PDEs
35A22 Transform methods (e.g., integral transforms) applied to PDEs


3rd-order PDE
Full Text: DOI


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