Soliton-like excitations in the one-dimensional electrical transmission line

Abstract

The dynamics of modulated waves are studied in the one-dimensional discrete nonlinear electrical transmission line. The contribution of the linear dispersive capacitance is taken into account, and it is shown via the reductive perturbation method that the evolution of such waves in this system is governed by the higher-order nonlinear Schrödinger equation. Passing through the Stokes analysis, we establish a generalized criterion for the Benjamin-Feir instability in the network and determine the exact solutions of the obtained wave equation by using the Pathria-Morris approach.

W-Shaped Bright Soliton of the (2 + 1)-Dimension Nonlinear Electrical Transmission Line

“…For JEFs, we consider the following assumption λ 1 = λ 3 = 0. We insert Equations ( 4) and ( 5) into Equation (2). After some algebraic manipulation with the help of MAPLE 18, we obtain:…”

“…Only a few systems, aside from these fields, allow for simple experimental observations. Nonlinear electrical transmission lines (NETLs) [2][3][4] are good illustrations of practical methods to examine how the nonlinear excitations behave within the nonlinear medium in physics.…”

Exact solitary wave solutions of a nonlinear Schrödinger equation model with saturable-like nonlinearities governing modulated waves in a discrete electrical lattice

“…Substituting Eqs. ( 17), (18), and (19) into Eq. ( 16), and equating the coefficients of each power of sin i (w) cos j (w) to zero, we obtain a system of algebraic equations for the parameters a 0 , a 1 , b 1 , v e , Ω , and µ, namely:…”

“…Nonlinear equations are widely used as models to describe many important dynamical phenomena in various fields of sciences, particularly in nonlinear optics, [1][2][3][4] in plasma physics, [5,6] in biophysics, [7] in Bose-Einstein condensates, [8] in atomic chain, [9,10] in Fermi-Pasta-Ulam lattice, [11,12] in crystals, [13][14][15][16] and in discrete electrical transmission lines. [17][18][19][20][21][22][23][24] Among these equations, the famous nonlinear Schrödinger (NLS) equation is usually derived from fundamental principles as a primary approximation. As such, its suitability for the accurate description of the phenomena of interest in these fields can be limited.…”

“…[26] Similarly, it has been used also to describe the dynamics of modulated waves in the specific case of the linear capacitor C s in the series branch, that is, for η = λ = 0. [18,27,28] Other special cases of this equation abound in the study of nonlinear discrete electrical transmission lines. [21,29] A basic approximation that is commonly made in investigating equations of this type consists in taking their solutions in the form A 0 exp(i(kn − ωt)) while assuming A 0 to be infinitesimally small.…”