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

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2013-07, Vol.88 (1), p.012909-012909, Article 012909
• Main Authors: Slunyaev, A, Pelinovsky, E, Sergeeva, A, Chabchoub, A, Hoffmann, N, Onorato, M, Akhmediev, N
• Format: Article
• Language: English
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/PhysRevE.88.012909

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.