In this paper, the mass transfer in a time varying thin liquid film over a stretching heated plate having variable temperature and concentration is analyzed. The analytical solution for the unsteady NavierStokes, energy and diffusion equations are obtained. A new similarity is found using group-theoretic analysis which renders the exact similar governing equations amenable to analytical solutio...

In this paper we study the stability of integrable Hamiltonian systems under small perturbations, proving a weak form of the KAM/Nekhoroshev theory for viscosity solutions of Hamilton-Jacobi equations. The main advantage of our approach is that only a finite number of terms in an asymptotic expansion are needed in order to obtain uniform control. Therefore there are no convergence issues involv...

in this paper, an application of homotopy perturbation method is appliedto nding the solutions of the seven-order sawada-kotera (ssk) and a lax'sseven-order kdv (lskdv) equations. then obtain the exact solitary-wave so-lutions and numerical solutions of the ssk and lskdv equations for the initialconditions. the numerical solutions are compared with the known analyticalsolutions. their rem...

in this paper, we adapt the operational tau method for personal computers and apply it to a system of two nonlinear second order ordinary differential equations which are related to general relativity. the interesting behaviour this problem exhibits in its numerical treatment is discussed. in this problem, we try to use the tau perturbation term to locate the correct solution of this nonlinear ...