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

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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.
Funding Information
  • National Natural Science Foundation of China (11501175)
  • Subsidy scheme for young backbone teachers of higher education institutions in He'nan Province (2015GGJS-080)

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