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

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

2010-10-11

arxiv.org/abs/1010.2046v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, contribution to the Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (4

Scientific paper

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.

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