Skew Adjoint Frechet derivative?

[Anthony]

Hi all,

I've been trying to construct a set of nonlinear PDEs:

$$P_\nu<u>=0, \qquad \nu = 1, \ldots , l</u>$$

that has skew-adjoint Frechet derivative, but with no luck. Is there any reason such a system of equations shouldn't exist? Here each $$P_\nu$$ is an analytic function of the coordinates on $$<u>\sim\mathrm{pr}^s (x,u)</u>$$, the s-th jet of $$(x,u)$$, where $$x=(x^1, \ldots , x^n)$$ and $$u = (u^1, \ldots , u^l)$$.

Any help would be much appreciated!

Ant

 

[Anthony]

Hold the phone - I think I've sorted it.