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 freq...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.展开更多
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 coeffic...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.展开更多
文摘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.
文摘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.
