An equation is derived that governs the evolution in two spatial dimensions of long internal waves in fluids of great depth. The equation is a natural generalization of Benjamin's (1967) one‐dimensional equation, and relates to it in the same way that the equation of Kadomtsev and Petviashvili relates to the Kortewegde‐Vries equation. The stability of one‐dimensional solitons with respect to long transverse disturbances is studied in the context of this equation. Solitons are found to be unstable with respect to such perturbations in any system in which the phase speed is a minimum (rather than a maximum) for the longest waves. Internal waves do not have this property, and are not unstable with respect to such perturba
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