A Class of PDEs with Nonlinear Superposition Principles

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.