![]() ![]() With the help of an optimal system, NLETLs convert into nonlinear ODE. The optimal system is computed by using the entire vector field and using the concept of abelian algebra. Then, we have to find the commutation relation of the entire vector field and observe that the obtained generators make an abelian algebra. ![]() The resulting equations concede two-dimensional Lie algebra. By using the group-theoretic technique, we analyse the NLETLs and compute infinitesimal generators. This research is based on computing the new wave packets and conserved quantities to the nonlinear low-pass electrical transmission lines (NLETLs) via the group-theoretic method. Many numbers of significant techniques for the analytical and stable soliton and wave patterns of physical models have presently been created with the help of Matlab, Mathematica, etc., such as the differential transformation technique, the modified exponential-function method, the (G /G)-expansion technique, the improved (G /G)-expansion technique, the rational (G /G) technique, the generalized Kudryashov method, the homotopy analysis scheme, the mean finite difference Monte-Carlo technique, the Hirota's bilinear technique, the approach of modified simple equation, the F-expansion technique, the Exp-function scheme, the sine-Gordon expansion scheme, the modified Kudryashov method, the extended trial Equation scheme, the improved tan(Ψ(η)/2)-expansion scheme, the first integral technique, the Adomian decomposition method, the exponential rational function technique, the rational function technique, the unified scheme, the generalized projective Riccati scheme, the multi-symplectic Runge-Kutta technique, the modified extended tanh scheme, the generalized unified technique, the modified auxiliary technique, and other many methods and details are described in. Finally, the matching between analytical and numerical schemes has been shown through some tables and figures. Many distinct and novel solutions have been obtained and sketched, along with different techniques to show more details of the model’s dynamical behavior. Still, it researches to compare the used schemes’ accuracy by applying the quintic-B-Spline scheme and the convergence between three methods. This paper’s aim exceeds the idea of just finding the traveling wave solution of the considered model. ![]() Previous measurements of such short pulses using techniques. We also discuss the problem of validating these measurements. The considered model is also known as the sub-10-fs-pulse propagation model used to describe these measurements’ implications for creating even shorter pulses. This paper investigates the analytical solutions of the well-known nonlinear Schrödinger (NLS) equation with the higher-order through three members of Kudryashov methods (the original Kudryashov method, modified Kudryashov method, and generalized Kudryashov method). ![]()
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