We consider a modified Noguchi electrical transmission line and examine the effects of a linear capacitance C(s) on the wave characteristics while considering the semidiscrete approximation. It appears that wave modulations in the network are governed by a dispersive nonlinear Schrödinger equation whose coefficients are shown to be a function of C(s). We show that the use of this linear capacitance makes the filter more selective. We also show that the width of the unstable regions increases while that of the stable regions decreases with C(s) adding consequently the width of the frequency domain where bright solitons exist. Furthermore, we establish the existence of one more region (compared to the work of Marquié et al. [Marquié et al., Phys. Rev. E 49, 828 (1994)]) in the dispersion curve that allows the motion of envelope solitons of higher frequency in the system. Numerical and experimental investigations done on the model confirm our analytical predictions.
The dynamics of modulated waves in a nonlinear bi-inductance transmission line with dissipative elements are examined. We show the existence of two frequency modes and carry out intensive investigations on the low frequency mode. Thanks to the multiple scales method, the behavior of these waves is investigated and the dissipative effects are analyzed. It appears that the dissipation coefficient increases with the carrier wave frequency. In the continuous approximation, we derive that the propagation of these waves is governed by the complex Ginzburg–Landau equation instead of the Korteweg–de-Vries equation as previously established. Asymptotic studies of the dynamics of plane waves in the line reveal the existence of three additional regions in the dispersion curve where the modulational phenomenon is observed. In the low frequency mode, we demonstrate that the network allows the propagation of dark and bright solitons. Numerical findings are in perfect agreement with the analytical predictions.
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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