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The rogue wave solutions (rational multi-breathers) of the nonlinearSchrodinger equation (NLS) are tested in numerical simulations of weaklynonlinear and fully nonlinear hydrodynamic equations. Only the lowest ordersolutions from 1 to 5 are considered. A higher accuracy of wave propagation inspace is reached using the modified NLS equation (MNLS) also known as theDysthe equation. This numerical modelling allowed us to directly comparesimulations with recent results of laboratory measurements in\cite{Chabchoub2012c}. In order to achieve even higher physical accuracy, weemployed fully nonlinear simulations of potential Euler equations. Thesesimulations provided us with basic characteristics of long time evolution ofrational solutions of the NLS equation in the case of near breaking conditions.The analytic NLS solutions are found to describe the actual wave dynamics ofsteep waves reasonably well.

Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations