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

2010/10/11 by O. O. Vaneeva, Vaneeva, O. O., R. O. Popovych +3
Mathematics · Physics and Astronomy · #35A30 #35C05 #35K57 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35A30 #msc:35C05 #msc:35K57 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1010.2046

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

arxiv created 2010/10/11 · arxiv updated 2010/10/12

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.

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