Deriving the 2D KdV Equation for Overcoming Nonlinear Theory Challenges

[hunt_mat]

Does anyone know of a derivation or has a reference to the derivation of the 2D KdV equation (known as the KP equation I believe). I have done the linear theory for this problem and the results look good but the next stage is the weakly nonlinear theory and I am having trouble with a certain aspect of it.

 

[Studiot]

Johnson 1980 Water waves and Kortweg de Vries equations. J Fluid Mech, 97, 701-19

 

[hunt_mat]

Okay, I can work with this, Cheers. As an aside I am trying to extend the derivation to include the effect of surface tension and an electrical field. I have done this for one dimension but I have yet to do this for two.

The odd thing is that I was in contact with Johnson about this and he never mentioned this paper of his, weird.

 

[Studiot]

I haven't seen the paper itself - it came from a footnote at the bottom of page16 "for a review of one and two dimensional KDV equations..." of Drazin and Johnson.
The book itself treats 2D but only in solutions not derivations.

 

[hunt_mat]

It's actually quite a good paper, it tells me how I can go about overcoming my problem with the derivation and in that sense it's a very good thing. The linear problem for the 3D case actually wasn't much harder than the 2D case. What took me a while was plotting the solutions but I have not overcome that and I have some very pretty wave pictures.