The differential form method is applied to study the wave equation with dissipation and extended to determine potential symmetries. The symmetry group are given and group invariant solutions associated to the symmetries are obtained.
An ideal fluid traversed in all direction by straight vortex filament. In the present paper, we obtain the most general solution of the one-dimensional partial differential equation for the motion of an isolated stretched vortex filament combines with both self induction and elasticity, in an ideal fluid, by computing the symmetry groups using the general prolongation formula for their infinitesimal generators of a groups of transformations. Several authors obtained solution of KG equation using different type of method [1], [2]. In recent year the authors Pelloni and Pinotsis[5], Plyukhin and Schofield[6], Rao and Kagoli[7] and Valery[9] worked for finding the solution of KG equation.
In the present paper we have obtained the one parameter groups and symmetry transformations associated to the classical symmetries of the Klein-Gordon (KG) equation, we have also constructed an optimal system of two dimensional sub-algebras of the KG equation which provides the preliminary classification of group invariant solutions and yield the most general group invariant solution.
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