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Peng, Li; Keying, Liu; Zuliang, Pan; Weizhou, Zhong

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

J. Appl. Math. 2012, Article ID 346824, 15 p. (2012).
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.

MSC:

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

Keywords:

3rd-order PDE
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\textit{L. Peng} et al., J. Appl. Math. 2012, Article ID 346824, 15 p. (2012; Zbl 1246.35021)
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