So, I've been doing background research for the past week about applying this program. The first topic I'm looking into is optics, and the book I'm reading about this is "Applications of Non-Linear Fiber Optics" by Govind P. Agrawal. The current application I'm working with involves not solitons, but continuous waves (I'll be doing solitons later). Specifically, the equation comes from nonlinear dispersion curves (detailing continuous wave beams). After solving a nonlinear coupled-mode equation by assuming constant refraction index and a model for the total power of the forward and backward propagating waves, we can derive the Nonlinear-Schroedinger Equation. Furthermore, using a multiple-scale method (more on that later), we can prove equivalence between the linear and nonlinear case using this equation (essentially, a part of the equations drops to 0 for the nonlinear case).
Once equivalence is demonstrated, we describe the equation and the variables within. I'll post the equation as it's written in Agrawal's book once I get the LaTex add-on on my computer (I've been having comp trouble all week). Once I get that on, I'll describe the variables and how we can manipulate the equation to demonstrate different physical properties.