Can a certain little-known 2+1 dimensional generalization of the KdV equation be solved using the inverse scattering transformation?

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R. Mark Bradley

Note that if we set u=U(X,T), where X = (cos theta)x + (sin theta) y and T= (cos theta) t, then we get U_T + U_XXX + U U_X = 0, which is the KdV equation. However, the disturbance is still one-dimensional --- it just depends on X. I'm that hoping that the equations could be solved for an arbitrary initial two-dimensional condition.