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A similarity analysis of a nonlinear fin equation has been carried out by M. Pakdemirli and A.Z. Sahin [Similarity analysis of a nonlinear fin equation, Appl. Math. Lett. (2005) (in press)]. 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(More)
We consider steady state temperature distribution in a homogeneous rectangular infinite plate the lower part of which is cooled by a fluid flowing at a constant velocity while the upper part satisfies the general mixed boundary conditions. The Wiener-Hopf method has been used to obtain the solution in the infinite series form and some special cases have(More)
The Fisher equation, which arises in the study of reaction diffusion waves in biology, does not display a high level of symmetry properties. Consequently, only travelling wave solutions are obtainable using the method of invariants. This has a direct bearing on studying perturbed forms of the equation which may arise from considering, e.g., damping or(More)
We investigate the direct and inverse problem associated with the torsional waves propagating in a cylinder. We analyse the usual wave equation as well as the damped wave equation and consider the problem of recovering the initial profile from the observations of the final profile. This inverse problem arises when experimental measurements are taken at any(More)
Noether symmetries provide conservation laws that are admitted by Lagrangians representing physical systems. For partial differential equation possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. In this paper we provide a systematic procedure for determining Noether symmetries and conserved vectors(More)
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