Nonlinear Modulation of Travelling Rolls in Magnetoconvection

Modulational dynamics of oscillatory travelling rolls in magnetoconvection is studied near the onset of a Hopf bifurcation. Using weakly nonlinear analysis, we derive an envelope equation of oscillatory travelling rolls in the plane perpendicular to an ambient vertical magnetic field.The envelope equation is the Davey-Stewartson (DS) equation with complex coefficients, from which we obtain criteria for the modulational (Benjamin-Feir) instability of oscillatory travelling rolls.