A dynamic equation for water waves in one horizontal dimension

We apply a canonical transformation to a water wave equation to remove cubic nonlinear terms and to drastically simplify fourth-order terms in the Hamiltonian. This transformation explicitly uses the vanishing exact four-wave interaction for water gravity waves for a 2D potential fluid. After transformation, the well-known but cumbersome Zakharov equation is drastically simplified and can be written in XX-space in a compact form. This new equation is very suitable for analytical studies and numerical simulations.

► We construct effective canonical transformation for water wave Hamiltonian. ► It removes cubic terms in the Hamiltonian and simplify fourth-order terms. ► This transformation allows to write down Hamiltonian in XX-space in compact way. ► This Hamiltonian is very suitable for analytical and numerical study.