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A note on a symmetry analysis and exact solutions of a nonlinear fin equation. (English) Zbl 1143.35311
Summary: A similarity analysis of a nonlinear fin equation has been carried out by M. Pakdemirli and A. Z. Sahin [Appl. Math. Lett. 19, No. 4, 378–384 (2006; Zbl 1114.80003)]. Here, we consider a further group theoretic analysis that leads to an alternative set of exact solutions or reduced equations with an emphasis on travelling wave solutions, steady state type solutions and solutions not appearing elsewhere.

MSC:
35C05 Solutions to PDEs in closed form
35A30 Geometric theory, characteristics, transformations in context of PDEs
35K55 Nonlinear parabolic equations
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
58J70 Invariance and symmetry properties for PDEs on manifolds
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