Abstract
Advantages and limitations of the nonlinear Schrödinger equation in describing the evolution of nonlinear water-wave groups
Highlights
In recent years, the nonlinear Schrodinger (NLS) equation has attracted considerable attention as a possible model for describing the evolution of wave trains in deep and intermediate-depth water
The nonlinear Schrodinger (NLS) equation has attracted considerable attention as a possible model for describing the evolution of wave trains in deep and intermediate-depth water. This interest is prompted by the existence of a special class of analytic solutions to the NLS equation, the socalled breathers. These envelope solitons are periodic in time and/or in space, and exhibit a modulation pattern in which an initially small hump in the envelope is amplified significantly due to the focusing properties of the deep-water NLS equation
The qualitative similarities between the NLS breather solutions and rogue waves prompted suggestions that the NLS breathers can serve as a prototype of rogue waves in the ocean [1]
Summary
The nonlinear Schrodinger (NLS) equation has attracted considerable attention as a possible model for describing the evolution of wave trains in deep and intermediate-depth water. This interest is prompted by the existence of a special class of analytic solutions to the NLS equation, the socalled breathers These envelope solitons are periodic in time and/or in space, and exhibit a modulation pattern in which an initially small hump in the envelope is amplified significantly due to the focusing properties of the deep-water NLS equation. This evolution pattern reminds observations of the so-called rogue, or freak, waves in the oceans. More advanced models describing evolution of nonlinear unidirectional water waves are considered
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