Conserved quantities and travelling wave profiles to the nonlinear transmission line via Lie group analysis
Muhammad Bilal Riaz, Adil Jhangeer, Khadijah M. Abualnaja, Muhammad Junaid-U-Rehman
Abstract
Abstract The nonlinear transmission line (NLTL) equations are significant nonlinear evolution equations (NLEEs) in nonlinear electrical transmission line (NLETL) regulation. The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>tanh</mml:mi> </mml:math> method is employed to compute some traveling wave patterns of the NLTL equation. The new extended direct algebraic method (NEDAM) is a viable and successful mathematical method to construct the traveling wave patterns of science and engineering problems. The NEDAM is effectively utilized to obtain the traveling wave structures of a considered model in the form of trigonometric and hyperbolic functions containing parameters. The Lie symmetry technique is used to analyze the NLTL equation and compute the Infinitesimal generators. Moreover, we have shown graphically obtained wave profiles by using the different suitable values of the parameters involved. Further, the nonlinear transmission line equation is described through nonlinear self-adjointness, and conserved quantities are computed for each vector.