You are right, i think so, but i'm not used with PDE interface of COMSOL and doing so requires some time. I tried to apply the nonlinear gradient as an equation that i defined in the global definitions, But COMSOL considers the temperature of the top and bottom surfaces to calculate and apply the linear gradient.
The attached examples are for the heat transfer module...the beam module is a solid mechanic one....i.e. the degree of freedoms of the beam module are the dispacement field components (u, v, w), while it is the temperature (T) in the heat transfer module.
I worked on the KP-BBM water waves equation in two directions and I have used comsol to verify the results obtained by Matlab using the finite difference method. I send you a scanned document and I hope that he will help you.