Soliton solutions and traveling wave solutions for a discrete electrical lattice with nonlinear dispersion through the generalized Riccati equation mapping method

A variety of new soliton structures and various dynamical behaviors of a discrete electrical lattice with nonlinear dispersion via variety of analytical architectures

“…$$$ \beta $$$ is related to the lower and upper cutoff mode frequencies. The authors in previous studies 40,43 have studied the model Equation () by the generalized Riccati equation mapping method, Kudryashov expansion method, and auxiliary equation method, respectively.…”

“…Using the continuum approximation and assuming that $$$ {u}_n $$$ changes slowly from one unit segment to the next, and replacing the discrete index $$$ n $$$ with a continuous variable $$$ x $$$, and using the Taylor expansion for the $$$ {u}_{n+1} $$$ with conditions $$$ {u}_n\ll 1 $$$, lead to the nonlinear model equation for the boundary driven bi‐inductance dispersive NLTL shown in Figure 1 as 40 $$$$ \frac{d^2u}{d{x}^2}-\left(\alpha -2\right)u+\left(\alpha +\frac{\beta }{\gamma}\right)\left({u}^3-{u}^5\right)=0. $$$$ …”

“…By changing the parameters, Equation (11) generates certain specific types of solutions, such as trigonometric, hyperbolic trigonometric, and rational function solutions. The generalized Riccati equation mapping method was utilized by the authors in an earlier study 40 to create the bright, dark, and optical solitons solutions of Equation (1). As a result, our solutions are novel and have never been presented before.…”

Automatic Distributed Control Method for Indoor Low-Voltage Electricity Based on Modal Symmetry Algorithm

“…In the process of control, a collection station is composed of several microprocessor cores [4][5][6]. It can organically combine computer technology, communication technology, display technology, and control technology, connects different functions and local computers, and has the advantages of good monitoring performance, high reliability, good expansibility, and easy maintenance [7][8][9]. With the interconnection of cross-regional power grids and constraints from economy and technology, in order to make the full use of existing system resources, power grids are often forced to operate near the critical point, and the voltage stability margin is very low, which increases the probability of power accidents such as voltage collapse [10][11][12].…”

Some newly explored exact solitary wave solutions to nonlinear inhomogeneous Murnaghan’s rod equation of fractional order

“…Tala-Tebue et al [30] used this method to solve discrete nonlinear electrical transmission lines in (2 + 1) dimension. Salathiel et al [31] utilized generalized Riccati equation mapping method to construct soliton and travelling wave solutions for discrete electrical lattice. Koonprasert et al [32] implemented this method to find more explicit solitary solutions to the space-time fractional fifth-order nonlinear Sawada-Kotera equation.…”