In Phys. D 78 (1994) 124, we have found that iterations of the nonclassical symmetries method give rise to new nonlinear equations, which inherit the Lie point symmetry algebra of the given equation. In the present paper, we show that special solutions of the right-order heir-equation correspond to classical and nonclassical symmetries of the original equations. An infinite number of nonlinear equations which possess nonclassical symmetries are derived. © 2003 Elsevier Science (USA). All rights reserved.
Nucci, M. C. (2003). Nonclassical symmetries as special solutions of heir-equations. Journal of Mathematical Analysis and Applications, 279(1), 168–179. https://doi.org/10.1016/S0022-247X(02)00706-0