-conditional symmetries [see I. W. Fushchich and W. M. Shtelen, Lett. Nuovo Cimento (2) 34, No. 16, 498–502 (1982); erratum ibid. 36, No. 4, 96 (1983; Zbl 0952.22002)] for two nonlinear reaction-diffusion-convection (RDC) equations with power diffusivities of the form
where and are arbitrary constants and is an arbitrary function are considered. The main results are presented in the form of two theorems.
Theorem 1: Equation (1) is -conditional invariant under the operator if and only if it and relevant operator have the following forms:
(i) , , ; ;
(ii) , ; ;
(iii) , ; ,
where , , , , , where , and are arbitrary constants. The obtained -conditional symmetries are applied for constructing a wide range of exact solutions of the nonlinear RDC equations.