# Super compact spatial and temporal equations for water waves

by some canonical transformation. We suggest a specific form of such transformation that allows one to derive a remarkably simple form of temporal and spatial equatios. One can name it the super compact equation. This equation is very straightforward and

includes a nonlinear wave term and advection term. Moreover, this equation also allows one to derive a spatial version of the water waves equation which can be used to describe experiments it the flume.

We derive very simple compact equations for unidirectional gravity water waves. For such waves, as it is well-known,

the coefficient of nontrivial four-wave interaction is identically zero. This fact allows one to essentially simplify

the Zakharov equation, applying a canonical transformation. Obviously this transformation is not unique. In this paper

we suggest a specific form of such transformation that allows one to derive a remarkably simple form of the Zakharov

equation. One can name it the super compact equation. This equation is very straightforward and

includes a nonlinear wave term (\`{a} la NLSE) and advection term. Moreover, this equation also allows one to derive a

spatial version of the water waves equation which can be used to describe experiments it the flume.