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

Deffo, Guy Roger; Yamgoué, Serge Bruno; Pelap, F. B.

doi:10.1016/j.chaos.2021.111397

Cited by 8 publications

(3 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equation (25) shows clearly that for σ = 0, the analytical expression of the bright-like soliton width is inversely proportional to the soliton amplitude χ 0 which is an independent function of time. It is the most crucial property of the bright soliton.…”

Section: Bright-like Solitary Wavementioning

confidence: 96%

“…The first nonlinear element is a varicap diode whose differential capacitance C(V b + V n ) = dQ n /dV n is a nonlinear function of the voltage V n . For low voltages around the dc bias voltage V b , Q n (V n ) at the (n)th node can be defined by [25,26]…”

Section: Model Description and Dynamic Equation 21 Model Presentationmentioning

confidence: 99%

“…( 5) and represent the angular frequency and group velocity, respectively. A(x, τ) corresponds to one of the above profiles, namely, the bright solitary solution (25) or the dark solitary solution (27). Next, for the effectiveness of these simulations, the network parameters (4) are exploited together with ε = 0.1 and χ 0 = 1.…”

Section: Dark Solitary Wavementioning

confidence: 99%

See 2 more Smart Citations

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

et al. 2023

View full text Add to dashboard Cite

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.

show abstract

Section: Bright-like Solitary Wavementioning

confidence: 96%

Section: Model Description and Dynamic Equation 21 Model Presentationmentioning

confidence: 99%