The modified version of the Schrödinger equation that describes deep water waves is known as the Nonlinear Schrödinger Equation (NLS). In fluid dynamics, this equation captures the evolution of complex wave envelopes in deep water and is particularly useful in modeling phenomena like rogue waves, solitons, and wave packet modulation. The deep-water version of the NLS is given by:

where:

The NLS effectively captures how wave packets in deep water undergo both dispersion (due to (\alpha)) and nonlinearity (due to (\beta)), creating a balance that can lead to stable structures like solitons or unstable ones like rogue waves. This version of the equation is essential in understanding how energy distributes within wave packets in deep water.