2006/08/07 by P. K. Shukla, I. Kourakis, B. Eliasson +2 · 1 citation
Physics and Astronomy · #nlin.CD
paper · pdf · doi:10.1103/physrevlett.97.094501
published as Phys. Rev. Lett. 97, 094501 (2006) · 4 pages, 4 figures, to appear in Physical Review Letters
arxiv created 2006/08/07 · arxiv updated 2009/12/01
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large amplitude freak waves in deep water.