Construction of new traveling and solitary wave solutions of a nonlinear PDE characterizing the nonlinear low-pass electrical transmission lines

Abstract

In this study, we intend to analyze the traveling and several other solitary wave solutions in the nonlinear low-pass electrical transmission line model using the new mapping method, the new extended auxiliary equation method, and the extended Kudryashov method. A type of traveling and solitary wave solutions emerge, consisting of hyperbolic function, trigonometric, rational, periodic, and doubly periodic solutions that reflect kink, anti-kink wave solitons, bright-dark optical solitons, singular solitons, and other traveling waves. The three integration techniques applied are efficient, effective, and versatile for the creation of new bright, dark, singular, and non-singular periodic and solitary wave propagation solutions in nonlinear low-pass electrical transmission lines. To see the extant physical significance of the considered equation, we present some 2D and 3D figures for some solutions. We compare the obtained results with those obtained in the literature. We investigate and demonstrate the stability of the soliton solutions.

Research on sensitivity analysis and traveling wave solutions of the (4 + 1)-dimensional nonlinear Fokas equation via three different techniques

“…The GEM, ERFM, and modified extended tanh-function methods will be used to generate some exact solitary wave solutions of the Fokas equation in this section. For reducing equation (1) to ODE, we will use wave transformation equation (3). For this situation differentiations of U respect to independent variables are given by; and similarly we obtain…”

“…Reduction to ordinary differential equations is usually based on Lie symmetries and wave transformations. In literature recent years, lots of methods are given for solving NPDEs for example the tanh-coth strategy [1], the auxiliary equation technique [2,3], modified simple equation technique [4], Bernoulli function methodology [5], the new extended direct algebraic technique [6], the sine-Gordon expansion technique [7,8], Hirota bilinear technique [9], the simplest extended equation technique [10,11], the F-expansion technique [12], He's semi-inverse technique [13], the sub-ODE technique [14], the (G'/G) -expansion technique [15], the generalized Kudryashov technique [16], and many more. The common point of all the methods mentioned here is to convert the PDEs to the ordinary differential equations (ODEs) with the help of wave transformations.…”

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

“…Therefore, for this purpose, some of the popular and direct techniques were presented such as the Riccati equation expansion method, the extended tanh method, the variational iteration method, the (G ′ ∕G)expansion method, the generalized Riccati equation mapping method, the exp-function method, the auxiliary equations methods, the Kudryashov method, the simplest equation method, the new modified sub-ordinary differential equation (ODE) method, Lie symmetry approach, and many other methods for extracting soliton solutions. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] Recent research has focused on N-soliton solutions for nonlocal integrable equations, such as Riemann-Hilbert problems for nonlocal integrable equations resulting from a single group reduction [27][28][29] and nonlocal integrable equations resulting from two group reductions. [30][31][32] In (1+1) and (2+1)-dimensional systems, a brief review of derived N-soliton solutions through the Hirota bilinear approach is provided.…”

“…Further, Nagashima and Amagishi were among the first to model the solitons propagation in the dispersive medium 7 . The NLTLs have been the subject of several investigations, 8–21 and the soliton solutions of the NLTL model equations became an important part of the research, currently. Therefore, for this purpose, some of the popular and direct techniques were presented such as the Riccati equation expansion method, the extended tanh method, the variational iteration method, the ( $$$ {G}^{\prime }/G $$$)‐ expansion method, the generalized Riccati equation mapping method, the exp‐function method, the auxiliary equations methods, the Kudryashov method, the simplest equation method, the new modified sub‐ordinary differential equation (ODE) method, Lie symmetry approach, and many other methods for extracting soliton solutions 8–26 .…”

“…The NLTLs have been the subject of several investigations, 8–21 and the soliton solutions of the NLTL model equations became an important part of the research, currently. Therefore, for this purpose, some of the popular and direct techniques were presented such as the Riccati equation expansion method, the extended tanh method, the variational iteration method, the ( $$$ {G}^{\prime }/G $$$)‐ expansion method, the generalized Riccati equation mapping method, the exp‐function method, the auxiliary equations methods, the Kudryashov method, the simplest equation method, the new modified sub‐ordinary differential equation (ODE) method, Lie symmetry approach, and many other methods for extracting soliton solutions 8–26 . Recent research has focused on N‐soliton solutions for nonlocal integrable equations, such as Riemann–Hilbert problems for nonlocal integrable equations resulting from a single group reduction 27–29 and nonlocal integrable equations resulting from two group reductions 30–32 .…”