Spatial Structures, Wave Fronts, Periodic Waves, Pulses and Solitary Waves in a One-Dimensional Array of Chua’s Circuits

2002 ◽  
pp. 77-164
Author(s):  
Vladimir I. Nekorkin ◽  
Manuel G. Velarde
Keyword(s):  
Solitary Waves ◽  
Periodic Waves ◽  
Spatial Structures ◽  
Wave Fronts ◽  
One Dimensional ◽  
Dimensional Array

TRAVELING WAVE FRONT AND ITS FAILURE IN A ONE-DIMENSIONAL ARRAY OF CHUA'S CIRCUITS

1993 ◽  
Vol 03 (01) ◽  
pp. 215-229 ◽  
Author(s):  
V. PEREZ-MUNUZURI ◽  
V. PEREZ-VILLAR ◽  
L. O. CHUA
Keyword(s):  
Traveling Wave ◽  
Diffusion Coefficients ◽  
Pulse Propagation ◽  
Critical Value ◽  
Nonlinear Phenomena ◽  
Wave Fronts ◽  
One Dimensional ◽  
Stirred Tank Reactors ◽  
Dimensional Array ◽  
Traveling Wave Front

Traveling wave fronts are considered for a one-dimensional array of Chua's circuits. This solution is obtained analytically and analyzed for the "primary real bifurcation". For diffusion coefficients less than some nonzero critical value it has been observed numerically that the traveling fronts fail to propagate. This nonlinear phenomena is similar to that observed from pulse propagation in nerves, and in coupled continuously-stirred tank reactors.

Homoclinic orbits and solitary waves in a one-dimensional array of Chua's circuits

1995 ◽  
Vol 42 (10) ◽  
pp. 785-801 ◽  
Author(s):  
V.I. Nekorkin ◽  
V.B. Kazantsev ◽  
N.F. Rulkov ◽  
M.G. Velarde ◽  
L.O. Chua
Keyword(s):  
Solitary Waves ◽  
Homoclinic Orbits ◽  
One Dimensional ◽  
Dimensional Array

scholarly journals Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Yun Wu ◽  
Zhengrong Liu
Keyword(s):  
Solitary Waves ◽  
Nonlinear Waves ◽  
Blow Up ◽  
Periodic Waves ◽  
The Third ◽  
Bifurcation Phenomena ◽  
Kink Waves ◽  
Fourth Kind

We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equationut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves.

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

MUTUAL EXCLUSION ON OPTICAL BUSES

2002 ◽  
Vol 12 (03n04) ◽  
pp. 341-358
Author(s):  
KRISHNA M. KAVI ◽  
DINESH P. MEHTA
Keyword(s):  
Mutual Exclusion ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Array ◽  
Propagation Delays ◽  
Optical Buses ◽  
The One

This paper presents two algorithms for mutual exclusion on optical bus architectures including the folded one-dimensional bus, the one-dimensional array with pipelined buses (1D APPB), and the two-dimensional array with pipelined buses (2D APPB). The first algorithm guarantees mutual exclusion, while the second guarantees both mutual exclusion and fairness. Both algorithms exploit the predictability of propagation delays in optical buses.

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.

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