Code to simulate the MMT model

Code to simulate the one-dimensional Majda-McLaughlin-Tabak (MMT) model used in

• Dù, R.S., Bühler, O., 2023. The Impact of Frequency Bandwidth on a One-Dimensional Model for Dispersive Wave Turbulence. J Nonlinear Sci 33, 81.

In short, the code solve the MMT model pseudospectrally using an Integrating Factor method with fourth-order-Runge–Kutta timestepping (IF-RK4). For more details, please refer to our paper.

To start, run outer_driver.m. This outer wrapper specifies some the key tunable parameteres of the MMT model, then it calls the main solver: MMT_solver.m.

The main solver then calls functions and subscripts in the folder SubRoutine. Here we list some key functions:

1. DNL_MMT.m: This function evaluate the nonlinear part of the MMT model. It is key for the pseudospectral solver.
2. RuntimePlotting_ForDiss.m: Subscript for plotting some information (e.g.: solution in real space, action spectrum, and integral quatities) about the MMT system as it evolves in time. Turn on runtime plotting by setting the doruntimeplots parameter in outer_driver.m.