Differential constraints and exact solutions of nonlinear diffusion equations

Abstract

The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries.

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• On the notion of conditional symmetry of differential equations
• Linear determining equations, differential constraints and invariant solutions
• Exact Solutions and Reductions of Nonlinear Diffusion PDEs of Pantograph Type
• Construction of complex solutions to nonlinear partial differential equations using simpler solutions