Discussion: some results from wave pulse experiments

Feir, J. E.

doi:10.1098/rspa.1967.0122

Cited by 57 publications

(8 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This equation seems to provide an accurate description of the evolution of a wave packet of small wave steepness e ¼ ak only for a limited time, at most O(e À2 ) wave periods. Feir (1967) confirmed experimentally this restriction on the validity of the NLS equation and confirmed that an initially symmetric wave packet of uniform frequency and moderate wave steepness eventually loses its symmetry as it propagates away from the wave maker and splits into two prominent groups of different frequencies. Later on Su (1982a, b) observed similar phenomena in his more comprehensive experiments with initially symmetric wave packets of uniform frequency and various durations.…”

Section: Higher-order Nonlinear Schrödinger Equationssupporting

confidence: 68%

Nonlinear Water Waves and Nonlinear Evolution Equations with Applications

Debnath¹,

Basu

2014

Encyclopedia of Complexity and Systems Science

View full text Add to dashboard Cite

Section: Higher-order Nonlinear Schrödinger Equationssupporting

confidence: 68%

Nonlinear Water Waves and Nonlinear Evolution Equations with Applications

Debnath¹,

Basu

2014

Encyclopedia of Complexity and Systems Science

View full text Add to dashboard Cite

“…Thus, our damping rate was comparable to Benjamin's. None of the other experimental papers on waves in deep water (Feir 1967;Melville 1982;Su 1982;Tulin & Waseda 1999;Trulsen & Stansberg 2001) reported measured damping rates.…”

Section: Comparison With Earlier Experimental Resultsmentioning

confidence: 99%

“…Experiments by Feir (1967), Yuen & Lake (1975), Su (1982), and Trulsen & Stansberg (2001) focused on the evolution of spatially localized wave packets, and these do not concern us here. Instead, we concentrate on experiments that involve modulations of a continuous train of nearly monochromatic waves, because they are consistent with the periodic boundary conditions used in this paper.…”

Section: Comparison With Earlier Experimental Resultsmentioning

confidence: 99%

Stabilizing the Benjamin–Feir instability

et al. 2005

View full text Add to dashboard Cite

The Benjamin-Feir instability is a modulational instability in which a uniform train of oscillatory waves of moderate amplitude loses energy to a small perturbation of other waves with nearly the same frequency and direction. The concept is well established in water waves, in plasmas and in optics. In each of these applications, the nonlinear Schrödinger equation is also well established as an approximate model based on the same assumptions as required for the derivation of the Benjamin-Feir theory: a narrow-banded spectrum of waves of moderate amplitude, propagating primarily in one direction in a dispersive medium with little or no dissipation. In this paper, we show that for waves with narrow bandwidth and moderate amplitude, any amount of dissipation (of a certain type) stabilizes the instability. We arrive at this stability result first by proving it rigorously for a damped version of the nonlinear Schrödinger equation, and then by confirming our theoretical predictions with laboratory experiments on waves of moderate amplitude in deep water. The Benjamin-Feir instability is often cited as the first step in a nonlinear process that spreads energy from an initially narrow bandwidth to a broader bandwidth. In this process, sidebands grow exponentially until nonlinear interactions eventually bound their growth. In the presence of damping, this process might still occur, but our work identifies another possibility: damping can stop the growth of perturbations before nonlinear interactions become important. In this case, if the perturbations are small enough initially, then they never grow large enough for nonlinear interactions to become important.

show abstract

“…A weakly nonlinear deep water wave train is unstable to long wave modulational perturbations, which is known as the Benjamin-Feir instability [1,2]. The long-time evolution of a twospace-dimensional wave packet is governed by the Davey-Stewartson (DS) equation [3][4][5][6] iu t + pu xx + u yy + r|u| 2…”

Section: Introductionmentioning

confidence: 99%

Quasi-line soliton interactions of the Davey–Stewartson I equation: on the existence of long-range interaction between two quasi-line solitons through a periodic soliton

Tajiri

Arai

2011

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

A periodic soliton is turned into a line soliton accordingly as a parameter point approaches to the boundary of the existing domain in the parameter space for a nonsingular periodic-soliton solution. We will call the periodic soliton with parameters of the neighborhood of the boundary a quasi-line soliton in this paper, which seems to be the line soliton. The interaction between two quasi-line solitons is the same as the interaction between two line solitons, except for very small parameter-sensitive regions. However, in such parameter regions, there are new long-range interactions between two quasi-line solitons through the periodic soliton as the messenger under some conditions, which cannot be described by the two-line-soliton solution.

show abstract

Discussion: some results from wave pulse experiments

Cited by 57 publications

References 1 publication

Nonlinear Water Waves and Nonlinear Evolution Equations with Applications

Nonlinear Water Waves and Nonlinear Evolution Equations with Applications

Stabilizing the Benjamin–Feir instability

Quasi-line soliton interactions of the Davey–Stewartson I equation: on the existence of long-range interaction between two quasi-line solitons through a periodic soliton

Contact Info

Product

Resources

About