Exact solitary wave solutions of a nonlinear Schrödinger equation model with saturable-like nonlinearities governing modulated waves in a discrete electrical lattice

Yamgoué, Serge Bruno; Deffo, Guy Roger; Tala-Tebue, E.; Pelap, F. B.

doi:10.1088/1674-1056/27/12/126303

Cited by 16 publications

(8 citation statements)

References 68 publications

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“…In the literature, many powerful techniques have been used to solve such an equation, and several types of solutions have been constructed. [41][42][43][44][45][46][47][48][49][50] Here, with the aid of the direct method, our attention is focused on the derivation of the solitary wave solutions of this equation. The kind of these solutions strongly depends on the sign of the product PQ as discussed below.…”

Section: Exact and Approximate Modulated Solitarymentioning

confidence: 99%

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

et al. 2023

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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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Section: Exact and Approximate Modulated Solitarymentioning

confidence: 99%

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

et al. 2023

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“…We aim to implement two powerful methods as follows the extended tanh method (Wazwaz 2007;Nuruddeen et al 2020;, and the Sine Gordon method Yamgoué et al 2018) to obtain new exact travelling wave solutions.…”

Section: Introductionmentioning

confidence: 99%

Computational and analytical solutions to modified Zakharov–Kuznetsov model with stability analysis via efficient techniques

Ali

Mehanna²

2021

Opt Quant Electron

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In this paper, we present the analytic and numerical solutions of the newly modified Zakharov-Kuznetsov equation. This model is used to study the waves in different plasmas. The analytical solutions were achieved by the extended tanh method and the Sine Gordon method while the numerical one is achieved by the implicit finite difference method and the local truncation error and the stability analysis for the difference scheme are given. Graphical representations of exact and numerical solutions are given to illustrate our results. In addition to the other known results in the literature, the paper contributes new analytical and numerical results.

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“…In the recent decades, nonlinear phenomena are continuously attracting the interest of researchers in several fields of sciences. [1][2][3][4][5][6] Within these studies, behavior of discrete nonlinear systems has been of great thoughtfulness in many areas of physics. Thus, discrete nonlinear transmission lines (NLTLs) are very useful tools for investigating dynamics of waves in nonlinear dispersive media.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

Ngounou¹,

Pelap²

2021

Chinese Phys. B

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This paper presents intensive investigation of dynamics of high frequency nonlinear modulated excitations in a damped bimodal lattice. The effects of the dissipation are considered through a linear dissipation coefficient whose evolution in terms of the carrier wave frequency is checked. There appears that the dissipation coefficient increases with the carrier wave frequency. In the linear limit and for high frequency waves, study of the asymptotic behavior of plane waves reveals the existence of two additional regions in the dispersion curve where the modulational phenomenon is observed compared to the lossless line. Based on the multiple scales method exploited in the continuum approximation using an appropriate decoupling ansatz for the voltage of the two different cells, it appears that the motion of modulated waves is described by a dissipative complex Ginzburg–Landau equation instead of a Korteweg–de Vries equation. We also show that this amplitude wave equation admits envelope and hole solitons in the high frequency mode. From basic sources, we design a programmable electronic generator of complex signals with desired characteristics, which delivers signals exploited as input waves for all our numerical simulations. These simulations are performed in the LTspice software that uses realistic components and give the results that corroborate perfectly our analytical predictions.

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Exact solitary wave solutions of a nonlinear Schrödinger equation model with saturable-like nonlinearities governing modulated waves in a discrete electrical lattice

Cited by 16 publications

References 68 publications

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

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

Computational and analytical solutions to modified Zakharov–Kuznetsov model with stability analysis via efficient techniques

Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

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