Dynamics of the plane and solitary waves in a Noguchi network: Effects of the nonlinear quadratic dispersion

Travelling waves in circuit chains are studied to measure continuous dispersion. A lock‐in frequency meter (LIF) is suitable for precisely determining k for each set of waves in finite alternate LC chains, where LIF has been proven to be more accurate than the fast Fourier transform. In addition to the –k measurement, the wave impedance spectrum of the travelling wave can be measured simultaneously, for investigating the dispersion and splitting of pulse propagation. The measured dispersion is validated to be consistent with the derived theoretical equations. The result provides an independent way to precisely obtain dynamical system properties for chains composed of non‐ideal components, such as resistors for researching non‐Hermitian behaviour under dissipation. Systematical mapping of relative deviation dependence of wave dispersion measurement with LIF on different chain length and component variation is studied, indicating boundaries of 1%, 0.1%, and 0.01% precision for guidance of experiments.

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Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

Ndoungalah

Deffo

Djine

et al. 2023

Chinese Phys. B

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In this paper, the control of dissipation and amplification of solitary waves in an electrical model of microtubule is demonstrated. This model is consisted of a shunt nonlinear resistance-capacitance ($J(V)-C(V)$) circuit and a series resistance-inductance $(R-L$) circuit. Through the linear dispersion analysis, two characters of the network are found, that is low band pass and bandpass characters. The effects of the conductance's parameter $\lambda$ on the linear dispersion curve are also analyzed. It appears that the increase of $\lambda$ induces a decrease (an increase) of the width of the bandpass filter for positive (negative) values of $\lambda$. By applying the reductive perturbation method, we derive the equation governing the dynamics of the modulated waves in the system. This obtained equation is the well-known nonlinear Schrödinger equation extended by a linear term proportional to an hybrid parameter $\sigma$, i.e. dissipation or amplification coefficient. Based on this parameter, we successfully demonstrate the hybrid behavior (dissipation and amplification) of the system. The exact and approximate solitary wave solutions of the obtained equation are derived and the effects of the coefficient $\sigma$ on the characteristic parameters of these waves are investigated. Using the found analytical solutions, we show numerically that the waves that are propagated throughout the system can be dissipated, amplified, or remained stable depending on the network parameters. These results are not only in agreement with the analytical predictions, but also with the existing experimental results in the literature.

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Dynamics of the plane and solitary waves in a Noguchi network: Effects of the nonlinear quadratic dispersion

Cited by 4 publications

References 30 publications

Bifurcation of solitary and periodic waves of an extended cubic-quintic Schrödinger equation with nonlinear dispersion effects governing modulated waves in a bandpass inductor-capacitor network

Bifurcation of solitary and periodic waves of an extended cubic-quintic Schrödinger equation with nonlinear dispersion effects governing modulated waves in a bandpass inductor-capacitor network

Wave propagation in finite discrete chains unravelled by virtual measurement of dispersion properties

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

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