A short remark on Kalaawy’s variational principle for plasma

Abstract

Purpose This paper aims to show how to establish a variational formulation directly from the governing equations. A modified Burger equation arising in dusty plasma is used as an example to show the derivation process. Design/methodology/approach Ji-Huan He’s semi-inverse method is adopted in the derivation process. To effectively use the semi-inverse method, a potential function is introduced, and the trial functional is constructed with some nonzero parameters, which are such identified that the stationary conditions satisfy the governing equations. Findings The derivation is simple, and the obtained variational principle is conciser than that obtained by Kalaawy, who introduced two special functions. Originality/value This paper suggests an effective approach to the inverse problem of the calculus of variations.