  The nonlinear Schrodinger equation is well known as a universal equation in
the study of wave motion. In the context of wave motion at the free surface of
an incompressible fluid, the equation accurately predicts the evolution of
modulated wave trains with low to moderate wave steepness. While there is an
abundance of studies investigating the reconstruction of the surface profile
$\eta$, and the fidelity of such profiles provided by the nonlinear Schrodinger
equation as predictions of real surface water waves, very few works have
focused on the associated flow field in the fluid. In the current work, it is
shown that the velocity potential $\phi$ can be reconstructed in a similar way
as the free-surface profile. This observation opens up a range of potential
applications since the nonlinear Schrodinger equation features fairly simple
closed-form solutions and can be solved numerically with comparatively little
effort. In particular, it is shown that particle trajectories in the fluid can
be described with relative ease not only in the context of the nonlinear
Schrodinger equation, but also in higher-order models such as the Dysthe
equation, and in models incorporating certain types of viscous effects.
