The Effect of a Magnetic Field on the Modulational Instability of Capillary-Gravity Waves

Abstract

Using the method of multiple scales, the propagation of quasi-harmonic capillary-gravity waves on a conducting fluid in the presence of a magnetic field is studied. The nonlinear Schrödinger equation governing amplitude modulation is derived and the stability condition is obtained. The effect of the magnetic field is to extend the stable region in the direction of small wave numbers.