Waves play a central role in many physical phenomena in plasma. For example, plasma that can be described by the incompressible MHD (magneto-hydrodynamics) equations with an external constant magnetic field gives rise to Alfven waves. In the limit of a very large magnetic field the Alfven waves form the leading term. For a moderate magnetic field, the Alfven waves interact with each other through the nonlinear interaction in MHD giving rise to wave turbulence. Similar phenomena appear in ocean waves. There are three key questions in the problems of wave turbulence: (1) what is the scaling of the energy spectrum ? (2) mixing and transport by turbulence ? (3) Non-Gaussian statistics or intermittency. In practice, numerically these are very difficult problems. They require simulations in three dimensions of nonlinear partial differential equations (PDEs) with very high resolution such that the scaling ranges are large enough to extract reliable scaling exponents. They also need to be run very long to be able to capture non-Gaussian statistics. I intend to study at very high resolution an one-dimensional model of wave turbulence, called the Majda-McLaughlin-Tabak model (MMT) [1] . The MMT model is particularly interesting because earlier works have shown that it cannot be captured by weak wave turbulence theories (quasi-Gaussian closures). In the last 25 years this model has been studied numerically but never in very high resolution, recent works have used 4096 grid points [2] . Recent works have not been able to reach very high resolution because they have not yet explored GPU computing for this problem. I intend to study it in very high resolution ( 2^20 grid points or more) and numerically settle conclusively the questions (1) to (3) above within this model. A GPU computing this the correct approach because even at very high resolution, by virtue of being one-dimensional, the required memory would fit in one single GPU card and the parallel computing capabilities of a single GPU card can be exploited to its maximum potential. [1] Majda, A.J., McLaughlin, D.W. and Tabak, E., 1997. A one-dimensional model for dispersive wave turbulence. Journal of Nonlinear Science, 7(1), pp.9-44. [2] Simonis, A. and Pan, Y., 2024. Transition from weak turbulence to collapse turbulence regimes in the Majda-McLaughlin-Tabak model. Physical Review E, 110(2), p.024202.