There surely is no rush to publish it, so you could keep it up your sleeve for a slow day.

I have found a classic, Whitham: "Linear and Nonlinear Waves", which has an extensive discussion of the Burgers equation and more generally equations of the form $u_t + f(u) u_x = 0$, and how to deduce general information about wavy solutions. Some part of that material would be a good crossover to some numerical results.