Question: manipulate a system of partial differential equation

HI to everybody, I have to manipulate a system of partial differential equation,one by one.how can I do? I have in particolat to derive a lot of time my differential equations(shallow water equations),and then to group, to substitute and at the and I need time derivative in function of spatial derivative. How is the best choice for working? I think to define for example:

pde := diff(q(x, y, t), t) +(g*D-u^2)*(diff(h(x, y, t), x))-2*u*(diff(q(x, y, t), x))=0

and then to derive pde. isn't it? And my main question is: there is a way to avoid to write the dependence of q from x,y,t for making the read more clear? I wasn't able to do it, if I define
q := q(x, y, t) it gives me an error, if I write
q = q(x, y, t)
when then I write

pde := diff(q, t)+(g*D-u^2)*(diff(h(x, y, t), x))-2*u*(diff(q, x)) = 0

it give me as result

(g*D-u^2)*(diff(h(x, y, t), x))=0

The best thing that I 'm able to do is to write Q = q(x, y, t) and then derive Q. But is not exactly what I want,because I want q (low case)for a lot of reason(then I create a latex and fortran files and I don't want to change all the name of variables!!). How can I do it?

Then I have to derive(I'm able top do it in maple) and substitute the value of a term(for example (diff(q, x))  that I get from another differential equation.how can I substitute this term?

thank so much
alberto from Venice