Conditional Lie–Bäcklund symmetries and sign-invariants to second-order evolution equations

The present paper discusses a class of second-order evolution equations which generalize reaction-diffusion–convection equations. It is shown that some equations admit of second-order conditional Lie–Bäcklund symmetries and first-order Hamilton–Jacobi sign-invariants, which preserve both signs, ⩾0⩾0 and ⩽0⩽0, on the solution manifold. Some examples are given to present the corresponding symmetry reductions, which reduce the considered equations to two-dimensional dynamical systems.

► This paper considers the second-order evolution equations. ► The conditional Lie–Bäcklund symmetries and the sign-invariants are obtained. ► The corresponding symmetry reductions are also presented.