I have obtained theoretically a solution to a nonlinear Schrödinger-type equation in dimension two. I also proved that is not constant. Now, I wonder if it depends on two variables and not only in one, that is, it is not one-dimensional. So my question is if *there exist some mathematical techniques in order to stablish that?*

I don't know any, so possible ways of proving it will be appreciated! Thanks in advance.

anyfunction $f(x,y)$ of two variables $x,y$ is also a function of a single variable $z=f(x,y)$? Perhaps you want to specify what relationship between $x$ and $y$ you would allow? $\endgroup$