A novel variational perturbation approach for formulating both linear and nonlinear acoustic model equations

Abstract

A novel approach, based on variational principles, for obtaining linear acoustic model equations directly from an arbitrary Lagrangian is presented, followed by extension to the case of weakly nonlinear acoustics. The efficacy and ease of application of the methodology adopted is demonstrated for two different Lagrangians: one describing classical potential flow, the other relativistic flow including viscous dissipation. It is shown, following appropriate simplification, that corresponding classical, well-known wave equations available in the open literature, derived in the recognised standard manner, are recovered.