Journal ArticleDOI
Nonlinear Modulation of Gravity Waves
Hidenori Hasimoto,Hiroaki Ono +1 more
TLDR
In this paper, a nonlinear plane wave solution to this equation is found to correspond to the so-called Stokes wave, and the linear stability of this plane wave is essentially determined by the sign of the product of two coefficients in this equation, yielding Benjamin and Whitham's criterion.Abstract:
Slow modulation of gravity waves on water layer with uniform depth is investigated by using singular perturbation methods. It is found, to the lowest order of perturbation, that the complicated system of equations governing such modulation can be reduced to a simple nonlinear Schrodinger equation. A nonlinear plane wave solution to this equation is found to correspond to the so-called Stokes wave. The linear stability of this plane wave solution is essentially determined by the sign of the product of two coefficients in this equation, yielding Benjamin and Whitham's criterion. The same equation is found to give a weak cnoidal wave derived from the Korteweg-de Vries equation in the shallow-water limit.read more
Citations
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Journal ArticleDOI
On three-dimensional packets of surface waves
A. Davey,Keith Stewartson +1 more
TL;DR: In this article, the authors used the method of multiple scales to derive the two coupled nonlinear partial differential equations which describe the evolution of a three-dimensional wavepacket of wavenumber k on water of finite depth.
Journal ArticleDOI
Rogue waves and their generating mechanisms in different physical contexts
TL;DR: In this paper, the authors introduce the concept of rogue waves, which is the name given by oceanographers to isolated large amplitude waves, that occur more frequently than expected for normal, Gaussian distributed, statistical events.
MonographDOI
Bäcklund and Darboux transformations : geometry and modern applications in soliton theory
Colin Rogers,Wolfgang K. Schief +1 more
TL;DR: Backlund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory have been explored in this article, where the authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Backlund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged.
Journal ArticleDOI
Nonlinear Four-Wave Interactions and Freak Waves
TL;DR: The theory of homogeneous four-wave interactions, extended to include effects of nonresonant transfer, compares favorably with the ensemble-averaged results of the Monte Carlo simulations as discussed by the authors.
Book
The Interaction of Ocean Waves and Wind
TL;DR: The Interaction of Ocean Waves and Wind describes the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days as discussed by the authors.
References
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Journal ArticleDOI
Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
Journal ArticleDOI
XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
D. J. de Korteweg,G. de Vries +1 more
TL;DR: In this article, the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves were discussed, and a new model of long wave propagation was proposed.
Journal ArticleDOI
The disintegration of wave trains on deep water Part 1. Theory
T. Brooke Benjamin,J. E. Feir +1 more
TL;DR: In this paper, a theoretical analysis of the stability of periodic wave trains to small disturbances in the form of a pair of side-band modes is presented, where the wave train becomes highly irregular far from its origin, even when the departures from periodicity are scarcely detectable at the start.
Journal ArticleDOI
Perturbation Method for a Nonlinear Wave Modulation. II
Tosiya Taniuti,Nobuo Yajima +1 more
TL;DR: In this paper, a perturbation method given in a previous paper of this series is applied to two physical examples, the electron plasma wave and a nonlinear Klein-Gordon equation.