TY - JOUR

T1 - Waves that appear from nowhere and disappear without a trace

AU - Akhmediev, N.

AU - Ankiewicz, A.

AU - Taki, M.

PY - 2009/2/2

Y1 - 2009/2/2

N2 - The title (WANDT) can be applied to two objects: rogue waves in the ocean and rational solutions of the nonlinear Schrödinger equation (NLSE). There is a hierarchy of rational solutions of 'focussing' NLSE with increasing order and with progressively increasing amplitude. As the equation can be applied to waves in the deep ocean, the solutions can describe "rogue waves" with virtually infinite amplitude. They can appear from smooth initial conditions that are only slightly perturbed in a special way, and are given by our exact solutions. Thus, a slight perturbation on the ocean surface can dramatically increase the amplitude of the singular wave event that appears as a result.

AB - The title (WANDT) can be applied to two objects: rogue waves in the ocean and rational solutions of the nonlinear Schrödinger equation (NLSE). There is a hierarchy of rational solutions of 'focussing' NLSE with increasing order and with progressively increasing amplitude. As the equation can be applied to waves in the deep ocean, the solutions can describe "rogue waves" with virtually infinite amplitude. They can appear from smooth initial conditions that are only slightly perturbed in a special way, and are given by our exact solutions. Thus, a slight perturbation on the ocean surface can dramatically increase the amplitude of the singular wave event that appears as a result.

UR - http://www.scopus.com/inward/record.url?scp=58149490756&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2008.12.036

DO - 10.1016/j.physleta.2008.12.036

M3 - Article

SN - 0375-9601

VL - 373

SP - 675

EP - 678

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 6

ER -