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

scholarly journals Numerical Modeling of the Interaction of Solitary Waves and Submerged Breakwaters with Sharp Vertical Edges Using One-Dimensional Beji & Nadaoka Extended Boussinesq Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mohammad H. Jabbari ◽  
Parviz Ghadimi ◽  
Ali Masoudi ◽  
Mohammad R. Baradaran
Keyword(s):  
Solitary Waves ◽  
Numerical Study ◽  
Time Integration ◽  
Boussinesq Equations ◽  
Linear Interpolation ◽  
Reflected Waves ◽  
One Dimensional ◽  
Propagating Waves ◽  
Linear Elements ◽  
Predictor Corrector

Using one-dimensional Beji & Nadaoka extended Boussinesq equation, a numerical study of solitary waves over submerged breakwaters has been conducted. Two different obstacles of rectangular as well as circular geometries over the seabed inside a channel have been considered in view of solitary waves passing by. Since these bars possess sharp vertical edges, they cannot directly be modeled by Boussinesq equations. Thus, sharply sloped lines over a short span have replaced the vertical sides, and the interactions of waves including reflection, transmission, and dispersion over the seabed with circular and rectangular shapes during the propagation have been investigated. In this numerical simulation, finite element scheme has been used for spatial discretization. Linear elements along with linear interpolation functions have been utilized for velocity components and the water surface elevation. For time integration, a fourth-order Adams-Bashforth-Moulton predictor-corrector method has been applied. Results indicate that neglecting the vertical edges and ignoring the vortex shedding would have minimal effect on the propagating waves and reflected waves with weak nonlinearity.

Solitary-wave solutions of nonlinear problems

1990 ◽  
Vol 331 (1617) ◽  
pp. 195-244 ◽  
Keyword(s):  
Fixed Point ◽  
Solitary Waves ◽  
Fixed Point Index ◽  
Fixed Point Theorems ◽  
Nonlinear Problems ◽  
One Dimensional ◽  
Propagating Waves ◽  
Model Equations ◽  
Permanent Form ◽  
General Method

A general method is presented for the exact treatment of analytical problems that have solutions representing solitary waves. The theoretical framework of the method is developed in abstract first, providing a range of fixed-point theorems and other useful resources. It is largely based on topological concepts, in particular the fixed-point index for compact mappings, and uses a version of positive-operator theory referred to Frechet spaces. Then three exemplary problems are treated in which steadily propagating waves of permanent form are known to be represented. The first covers a class of one-dimensional model equations that generalizes the classic Korteweg—de Vries equation. The second concerns two-dimensional wave motions in an incompressible but density-stratified heavy fluid. The third problem describes solitary waves on water in a uniform canal.

scholarly journals One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides

1996 ◽  
Vol 53 (1) ◽  
pp. 1138-1141 ◽  
Author(s):  
Roland Schiek ◽  
Yongsoon Baek ◽  
George I. Stegeman
Keyword(s):  
Solitary Waves ◽  
Second Order ◽  
Planar Waveguides ◽  
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

scholarly journals Existence of Solitary Waves in One Dimensional Peridynamics

2018 ◽  
Vol 136 (2) ◽  
pp. 207-236
Author(s):  
Robert L. Pego ◽  
Truong-Son Van
Keyword(s):  
Solitary Waves ◽  
One Dimensional

scholarly journals Circular dispersive shock waves in colloidal media

2016 ◽  
Vol 25 (04) ◽  
pp. 1650044 ◽  
Author(s):  
A. Azmi ◽  
T. R. Marchant
Keyword(s):  
Solitary Waves ◽  
Numerical Solutions ◽  
Particle Density ◽  
Modulational Instability ◽  
Particle Interaction ◽  
Packing Fraction ◽  
Effect Of Temperature ◽  
Hard Sphere Model ◽  
Large Radius ◽  
Temperature Dependent

A dispersive shock wave (DSW), with a circular geometry, is studied in a colloidal medium. The colloidal particle interaction is based on the repulsive theoretical hard sphere model, where a series in the particle density, or packing fraction is used for the compressibility. Experimental results show that the particle interactions are temperature dependent and can be either repulsive or attractive, so the second term in the compressibility series is modified to allow for temperature dependent effects, using a power-law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump in electric field amplitude is resolved via a DSW, which forms before the onset of modulational instability. A semi-analytical solution for the amplitude of the solitary waves in a DSW of large radius, is derived based on a combination of conservation laws and geometrical considerations. The effect of temperature and background packing fraction on the evolution of the DSW and the amplitude of the solitary waves is discussed and the semi-analytical solutions are found to be very accurate, when compared with numerical solutions.

Nonlinear waves in compacting media

1986 ◽  
Vol 164 ◽  
pp. 429-448 ◽  
Author(s):  
Victor Barcilon ◽  
Frank M. Richter
Keyword(s):  
Mathematical Model ◽  
Solitary Waves ◽  
Nonlinear Waves ◽  
Nonlinear Interaction ◽  
Phase Speed ◽  
Governing Equations ◽  
One Dimensional ◽  
The Earth ◽  
Permanent Shape ◽  
The Mathematical Model

An investigation of the mathematical model of a compacting medium proposed by McKenzie (1984) for the purpose of understanding the migration and segregation of melts in the Earth is presented. The numerical observation that the governing equations admit solutions in the form of nonlinear one-dimensional waves of permanent shape is confirmed analytically. The properties of these solitary waves are presented, namely phase speed as a function of melt content, nonlinear interaction and conservation quantities. The information at hand suggests that these waves are not solitons.

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
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