Author(s): H. S. Chiu; K. W. Chow; C. H. Tsang
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Abstract: Freak or rogue waves are waves of large amplitude arising from an otherwise relatively tranquil ocean surface. Waves with amplitude two or three times larger than normally expected in such background states may strike passenger and transport vessels, offshore and coastal structures. Breathers/homoclinic solutions of the nonlinear Schrodinger equation can be employed as models for freak waves: (1) The stability of the time periodic breather (Ma-breather) will be tested by direct numerical simulations with the split step Fourier methods. (2) The stability of the algebraic breather, which is localized in both time and space, will be examined. For waves of sufficiently large steepness, derivative nonlinear Schrodinger equations are considered. Exact form of breather solution of these higher order equations in special frame of reference will be presented.
Year: 2009