A VARIATIONAL PRINCIPLE FOR LINEAR AND NONLINEAR-WAVE PROPAGATION IN A DISSIPATIVE MEDIUM

In this paper we will give a variational principle with a vanishing parameter which provides a satisfactory variational characterization of dissipative systems. We will incorporate this variational principle into Whitman's averaged Lagrangian method to develop a formulation for the propagation of a slowly-varying wavetrain in a dissipative medium. We will then apply this formulation to describe the nonlinear evolution of a modulated gravity wave packet on the surface of a dissipative fluid and show that the modulation is stabilized by the dissipative effects.