Dissipative Discrete System with Nearest-Neighbor Interaction for the Nonlinear Electrical Lattice

Abdoulkary, Saïdou; Béda, Tibi; Doka, Serge Y.; Ndzana, Fabien Ii; Kavitha, L.; Mohamadou, Alidou

doi:10.4236/jmp.2012.36060

Cited by 16 publications

(9 citation statements)

References 37 publications

(44 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[26] In inhomogeneous nonlinear systems, MI may be considered as the leading mechanism for energy localization as well as the formation of traveling intrinsic localized modes. [27] In the NLS models, this phenomenon occurs if the product PQ is positive. In fact, the nonlinear dispersion relation is given by…”

Section: Generalitiesmentioning

confidence: 99%

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

et al. 2020

View full text Add to dashboard Cite

We consider a modified Noguchi network and study the impact of the nonlinear quadratic dispersion on the dynamics of modulated waves. In the semi-discrete limit, we show that the dynamics of these waves are governed by a nonlinear cubic Schrödinger equation. From the graphical analysis of the coefficients of this equation, it appears that the nonlinear quadratic dispersion counterbalances the effects of the linear dispersion in the frequency domain. Moreover, we establish that this nonlinear quadratic dispersion provokes the disappearance of some regions of modulational instability in the dispersion curve compared to the results earlier obtained by Pelap et al. (Phys. Rev. E 91 022925 (2015)). We also find that the nonlinear quadratic dispersion limit considerably affects the nature, stability, and characteristics of the waves which propagate through the system. Furthermore, the results of the numerical simulations performed on the exact equations describing the network are found to be in good agreement with the analytical predictions.

show abstract

Section: Generalitiesmentioning

confidence: 99%

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

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Recently, Abdoulkary et al considered the dynamics of a dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance and showed that the wave propagation is described by a generalized dissipative discrete complex Ginzburg-Landau equation. [15] They established the generalized discrete Lange-Newell criterion for MI phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear continuous bi-inductance electrical line with dissipative elements: Dynamics of the low frequency modulated waves

Ngounou

Pelap

2020

Chinese Phys. B

View full text Add to dashboard Cite

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.

show abstract

“…These are probably the reasons why, since pioneering works by Hirota and Suzuki [6] on electrical transmission lines simulating Toda lattice, a growing interest has been devoted to the use of nonlinear transmission lines, in particular, for studying nonlinear waves and nonlinear modulated waves: pulse solitons, envelope pulse (bright), hole (dark) solitons and kink and anti-kink solitons, [7][8][9] intrinsic localized modes (also called discrete breathers), [10][11][12] modulational instability. [13][14][15][16][17] Several methods for finding the exact solutions of nonlinear evolution equations for mathematical physics have been proposed, [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] such as Jacobian elliptic function method, [35,36] Fibonacci tanh function for NDDEs, [37] Expfunction method, [38,39] variable-coefficient discrete (G /G)expansion method for NDDEs, [40] and so on. In order to establish the effectiveness and reliability of the (G /G)-expansion method and to expand the possibility of its application, further research has been carried out by a considerable number of researchers.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of the nonlinear differential—difference equations associated with the nonlinear electrical transmission line through a variable-coefficient discrete (G′/G)-expansion method

Abdoulkary¹,

Mohamadou²,

Dafounansou³

et al. 2014

Chinese Phys. B

Self Cite

View full text Add to dashboard Cite

We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete (G /G)-expansion method, we solve the nonlinear differentialdifference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.

show abstract

Dissipative Discrete System with Nearest-Neighbor Interaction for the Nonlinear Electrical Lattice

Cited by 16 publications

References 37 publications

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

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

Nonlinear continuous bi-inductance electrical line with dissipative elements: Dynamics of the low frequency modulated waves

Exact solutions of the nonlinear differential—difference equations associated with the nonlinear electrical transmission line through a variable-coefficient discrete (G′/G)-expansion method

Contact Info

Product

Resources

About