Klein-Gordon equation in ideal fluid

Abstract

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.