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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)

This paper determines the conservation laws of the coupled Klein-Gordon equations that arise in the quantum field theory. There are two types of nonlinearity that will be considered, namely the cubic law and the power law. The Lie symmetry analysis with multiplier approach will be the mathematical tool that will be adopted to extract the conserved… (More)

- Ashfaque H Bokhari, Ahmad Y Dweik, F D Zaman, A H Kara, F M Mahomed
- 2009

In a recent work [1, 2] Sjöberg remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to find invariant solution for a non linear system of qth order partial differential equations with n independent and m… (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)

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)

- F D Zaman, R Al-Khairy
- 1999

We consider the temperature distribution in an infinite plate composed of two dissimilar materials. We suppose that half of the upper surface (y h,-oc < x < 0) satisfies the general boundary condition of the Neu-mann type, while the other half (y h,0 < x < oc) satisfies the general boundary condition of the Dirichlet type. Such a plate is allowed to cool… (More)

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