Universal geometric condition for the transverse instability of solitary waves

Transverse instabilities correspond to a class of perturbations traveling i n a direction transverse to the direction of the basic solitary wave. Solit ary waves traveling in one space direction generally come in one-parameter families. We embed them in a two-parameter family and deduce a new geometri c condition for transverse instability of solitary waves. This condition is universal in the sense that it does not require explicit properties of the solitary wave-or the governing equation. In this paper the basic idea is p resented and applied to the Zakharov-Kuznetsov equation for illustration. A n indication of how the theory applies to a large class of equations in phy sics and oceanography is also discussed.