What is the syntax for modelling a non-linear element in Spice?
In LTSPice you use behaviour models which have the prefix B. For voltage it is typically BV and for Current BI, here you need a BV type source. Look in ltwiki.org.

You can even implement laplace transforms directly as well as well as many different mathematical operations including differentiation etc.

Just scroll down the page, the website rendering is not the best.

Here is a screen shot of the component configuration editor from one of my sims implementing an integrator. (idt)