Transverse Stability in the Discrete Inductance-Capacitance Electrical Network

Tala-Tebue, E.; Kenfack-Jiotsa, A.

doi:10.4236/jmp.2013.46101

Cited by 8 publications

(2 citation statements)

References 19 publications

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“…In the network, nonlinearity is introduced by a varicap diode which admits that the capacitance varies with the applied voltage. The voltage V n m , and the nonlinear electrical charge Q n m , at the ( ) n m th , are related by the polynomial form given by [53][54][55]:…”

Section: Model Description and Circuit Equations 21 Model Presentationmentioning

confidence: 99%

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

2021

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In this work, the propagation of modulated waves in a nonlinear two-dimensional discrete electrical line is studied. Based on the linear dispersive law, we demonstrate that the network can adopt Hybrid’s behavior due to the fact that, without changing its appearance structure or its parameters values, it can become alternatively, a purely right-handed line, a purely left-handed line or a composite right-left-handed line depending on coupling transverse parameters L 2 , C 2 and k 2 . Using the reductive perturbation method, a (2+1)-dimensional nonlinear Schrodinger equation governing the dynamics of the small amplitude signals in the network is derived and the impact of the above transverse parameters on the sign of the product of their coefficients is examined. Likewise, backward and forward solitary wave propagations in the system is predicted and analyzed quantitatively and qualitatively. The effects of relevant transverse network parameters on the characteristic parameters of these waves are investigated. We find out that these transverse parameters considerably affect the characteristics and the nature of the waves that are propagated throughout the system.

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Section: Model Description and Circuit Equations 21 Model Presentationmentioning

confidence: 99%

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

2021

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“…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

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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.

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