Reduction operators of variable coefficient semilinear diffusion equations with an exponential source

Abstract

Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x{)}_x+h(x)e^{mu}$ are investigated using the algorithm involving a mapping between classes of differential equations, which is generated by a family of point transformations. A special attention is paid for checking whether reduction operators are inequivalent to Lie symmetry operators. The derived reduction operators are applied to construction of exact solutions.

13 pages, contribution to the Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (4 - 10 June 2010, Protaras, Cyprus)

References in corpus (5)

• Enhanced group analysis and conservation laws of variable coefficient reaction-diffusion equations with power nonlinearities
• A precise definition of reduction of partial differential equations
• Potential Nonclassical Symmetries and Solutions of Fast Diffusion Equation
• Is a nonclassical symmetry a symmetry?
• Group classification via mapping between classes: an example of semilinear reaction-diffusion equations with exponential nonlinearity

Cited by in corpus (3)

• Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities
• Generalized conditional symmetries of evolution equations
• Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions