Abstract
The propagation of quasi-monochromatic wave packets in a rarefied polydispersed mixture of a weakly compressible liquid with a finite number of fractions of differently sized gas bubbles is considered. Two equations for the modulation waves are derived by the multi-scale method in the cubic approximation in the wave amplitude: the non-linear Schrödinger equation ignoring dissipation effects and the Landau-Ginzburg equation for low dissipation due to the viscosity of the liquid and heat losses associated with bubble vibration. The coefficients of the non-linear Schrödinger equation are investigated to analyse the non-linear (modulational) stability of waves in a monodispersed non-dissipative bubble medium.
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