An electrical model for the Korteweg–de Vries equation

Giambò, Sebastiano; Pantano, Pietro; Tucci, P.

doi:10.1119/1.13685

Cited by 17 publications

(7 citation statements)

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“…where the velocity ẋ(t) is obtained by using Eq. (14). For e = 1 (i.e., the separatrix orbit with m = 1), the phase-portrait coordinates become…”

Section: B Motion In a Quartic Potentialmentioning

confidence: 99%

A primer on elliptic functions with applications in classical mechanics

Brizard

2009

Eur. J. Phys.

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The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi), the motion of a force-free asymmetric top (Jacobi), the motion of a spherical pendulum (Weierstrass), and the motion of a heavy symmetric top with one fixed point (Weierstrass). The problem of the planar pendulum, in fact, can be used to construct the general connection between the Jacobi and Weierstrass elliptic functions. The easy access to mathematical software by physics students suggests that they might reappear as useful tools in the undergraduate curriculum.

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“…where the velocity ẋ(t) is obtained by using Eq. (14). For e = 1 (i.e., the separatrix orbit with m = 1), the phase-portrait coordinates become…”

Section: B Motion In a Quartic Potentialmentioning

confidence: 99%

A primer on elliptic functions with applications in classical mechanics

Brizard

2009

Eur. J. Phys.

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“…Simulating (4) and assuming an initial function such as a Gaussian function, we observe the emergence of traveling waves as shown in Figure 3.…”

Section: Cnn Transmission Linesmentioning

confidence: 98%

“…Considering two transmission lines that intersect in a given cell ( , ), called cross cell, as in Figure 4, the state of each cell, except for cross cell ( , ), is governed by (4). Not only does the neighborhood of cross cell ( , ) consist of the two cells at its left and right, respectively but also it is made up of its upper and lower cells.…”

Section: Cnn Transmission Linesmentioning

confidence: 99%

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Simulation, Modeling, and Analysis of Soliton Waves Interaction and Propagation in CNN Transmission Lines for Innovative Data Communication and Processing

Borgese

Vena

Pantano

et al. 2015

Discrete Dynamics in Nature and Society

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We present an innovative approach to study the interaction between oblique solitons, using nonlinear transmission lines, based on Cellular Neural Network (CNN) paradigm. A single transmission line consists of a 1D array of cells that interact with neighboring cells, through both linear and nonlinear connections. Each cell is controlled by a nonlinear Ordinary Differential Equation, in particular the Korteweg de Vries equation, which defines the cell status and behavior. Two typologies of CNN transmission lines are modelled: crisscross and ring lines. In order to solve KdV equations two different methods are used: 4th-order Runge-Kutta and Forward Euler methods. This is done to evaluate their accuracy and stability with the purpose of implementing CNN transmission lines on embedded systems such as FPGA and microcontrollers. Simulation/analysis Graphic User Interface platforms are designed to conduct numerical simulations and to display elaboration results. From this analysis it is possible both to identify the presence and the propagation of soliton waves on the transmission lines and to highlight the interaction between solitons and rich nonlinear dynamics. With this approach it is possible to simulate and develop the transmission and processing of information within large brain networks and high density sensor systems.

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“…The dynamical properties of amplitude dependent inertial masses for strongly non-separable modes in a nonlinear vibrational lattice have not yet been treated; however, nonlinear lumped element electrical transmission line studies have a long history [17][18][19] and there is a well known translation between inertial mass and electrical inductance for such linear transmission lines 20 . As long as electrical pulses extend over many nonlinear elements of an electrical transmission line so that continuum equations, such as the Korteweg-de Vries, could be applied it has been possible to make contact with soliton behavior [21][22][23][24][25] . In more recent times interest has shifted from understanding soliton behavior to the production of high frequency radiation using electromagnetic shock waves produced by hysteresis in nonlinear electric lines [26][27][28] .…”

Section: Introductionmentioning

confidence: 99%

Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line

et al. 2016

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The experimental properties of intrinsic localized modes (ILMs) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest-neighbor intersite potentials. Here it is shown for a one-dimensional lumped electrical transmission line that a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis, the nonlinear inductive current equations are transformed to flux transmission line equations with analog onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice, ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally, this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.

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An electrical model for the Korteweg–de Vries equation

Cited by 17 publications

References 0 publications

A primer on elliptic functions with applications in classical mechanics

A primer on elliptic functions with applications in classical mechanics

Simulation, Modeling, and Analysis of Soliton Waves Interaction and Propagation in CNN Transmission Lines for Innovative Data Communication and Processing

Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line

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