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 determine the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the governing PDE is proved C-integrable. In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation.
Li Peng. Liu Keying. Pan Zuliang. Zhong Weizhou. "A Class of PDEs with Nonlinear Superposition Principles." J. Appl. Math. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/346824