One-Dimensional Modulational Instability in a Crossed-Field Gap

1996 ◽  
Vol 76 (18) ◽  
pp. 3324-3327 ◽  
Author(s):  
Peggy J. Christenson ◽  
Y. Y. Lau
Keyword(s):  
Modulational Instability ◽  
One Dimensional

Modulational instability and solitary waves in one-dimensional lattices with intensity-resonant nonlinearity

2008 ◽  
Vol 78 (4) ◽  
Author(s):  
Milutin Stepić ◽  
Aleksandra Maluckov ◽  
Marija Stojanović ◽  
Feng Chen ◽  
Detlef Kip
Keyword(s):  
Solitary Waves ◽  
Modulational Instability ◽  
One Dimensional

Spatial modulational instability in one-dimensional lithium niobate slab waveguides

2000 ◽  
Vol 25 (24) ◽  
pp. 1786 ◽  
Author(s):  
H. Fang ◽  
R. Malendevich ◽  
R. Schiek ◽  
G. I. Stegeman
Keyword(s):  
Lithium Niobate ◽  
Modulational Instability ◽  
One Dimensional ◽  
Slab Waveguides

LOCALIZED BREATHER-LIKE EXCITATIONS IN THE HELICOIDAL PEYRARD–BISHOP MODEL OF DNA

2009 ◽  
Vol 02 (04) ◽  
pp. 405-417 ◽  
Author(s):  
CONRAD BERTRAND TABI ◽  
ALIDOU MOHAMADOU ◽  
TIMOLEON CREPIN KOFANE
Keyword(s):  
Analytical Solution ◽  
Continuous Wave ◽  
Exact Analytical Solution ◽  
Modulational Instability ◽  
Elliptic Functions ◽  
Instability Criterion ◽  
Dna Dynamics ◽  
Jacobian Elliptic Functions ◽  
One Dimensional ◽  
The One

We consider the one-dimensional helicoidal Peyrard–Bishop (PB) model of DNA dynamics. By means of a method based on the Jacobian elliptic functions, we obtain the exact analytical solution which describes the modulational instability and the propagation of a bright solitary wave on a continuous wave background. It is shown that these solutions depend on the modulational (or Benjamin-Feir) instability criterion. Numerical simulations of their propagation show these excitations to be long-lived and suggest that they are physically relevant for DNA.

Diffraction and Instability of Short-Crested Limited-Length One-Dimensional Coherent Wave Trains

2015 ◽  
Author(s):  
Alexander V. Babanin ◽  
Takuji Waseda
Keyword(s):  
Modulational Instability ◽  
Three Dimensional ◽  
Lateral Spread ◽  
Wave Tank ◽  
One Dimensional ◽  
Coherent Wave ◽  
Limited Length ◽  
Lateral Extent ◽  
Wave Trains ◽  
The University

Alternative representations of the wave field (as opposed to superposition of Fourier components) are possible. In this paper, behaviour of short-crested limited-length one-dimensional coherent wave trains is investigated. Experiments were conducted in the three-dimensional wave tank of the University of Tokyo. Description of the directional wave tank and its capacity to generate short-crested coherent wave trains, including those concurrent, superposed and directionally-superposed is provided. If the crest is shorter than the lateral extent of the wave tank, diffraction tends to redistribute the wave energy into clear surfaces, and thus energy of the wave trains is reduced and the modulational instability bandwidth changes correspondingly. Rates of such nonlinear lateral spread are estimated, and they are proportional to mean wave steepness. To avoid the diffraction, in further tests concurrent trains were mechanically generated, each of which occupied half of the lateral width of the wave tank and had the same energy as another half. The trains had the same frequency, and in order to keep them separate phase shift of 180 degrees was used. Sideband growth was significantly impaired by comparison with the long-crested evolution of the train with the same steepness.

Modulational instability and rogue waves in one-dimensional nonlinear acoustic metamaterials: case of diatomic model

2021 ◽  
Author(s):  
Joseph Mora ◽  
Justin Mibaile ◽  
Vroumsia David ◽  
Sylvere Azakine ◽  
Gambo Betchewe
Keyword(s):  
Integrable System ◽  
Taylor Series ◽  
Acoustic Waves ◽  
Perturbation Methods ◽  
Modulational Instability ◽  
Rogue Waves ◽  
Acoustic Metamaterials ◽  
One Dimensional ◽  
Acoustic Metamaterial ◽  
Nonlinear Acoustic

Abstract In this paper, by means of the expanded Taylor series and Lindstedt-Poincar ́e perturbation methods, the coupled nonlinear Schrödinger equations (CNLSE) modeling the propagation of acoustic waves in acoustic metamaterial is obtained. Using these equations, the Modulational Instability (MI) phenomenon is observed in disturbance mode. Manakov integrable system is derived with suitable parameters and we shown that the Rogue Waves (RWs) can propagate diatomic acoustic metamaterials.

Sign in / Sign up

Export Citation Format

Share Document