Second-Order Conditional Lie–Bäcklund Symmetries and Differential Constraints of Nonlinear Reaction–Diffusion Equations with Gradient-Dependent Diffusivity

Abstract

The radially symmetric nonlinear reaction–diffusion equation with gradient-dependent diffusivity is investigated. We obtain conditions under which the equations admit second-order conditional Lie–Bäcklund symmetries and first-order Hamilton–Jacobi sign-invariants which preserve both signs (≥0 and ≤0) on the solution manifold. The corresponding reductions of the resulting equations are established due to the compatibility of the invariant surface conditions and the governing equations.

Keywords

• conditional Lie–Bäcklund symmetry
• differential constraint
• sign-invariant
• nonlinear reaction–diffusion equation
• symmetry reduction