Abstract
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. By using the group-theoretic technique, we analyse the NLETLs and compute infinitesimal generators. The resulting equations concede two-dimensional Lie 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 optimal system is computed by using the entire vector field and using the concept of abelian algebra. With the help of an optimal system, NLETLs convert into nonlinear ODE. The modified Khater method (MKM) is used to find the wave packets by using the resulting ODEs for a supposed model. To represent the physical importance of the considered model, some 3D, 2D, and density diagrams of acquired results are plotted by using Mathematica under the suitable choice of involving parameter values. Furthermore, all derived results were verified by putting them back into the assumed equation with the aid of Maple software. Further, the conservation laws of NLETLs are computed by the multiplier method.
Highlights
The nonlinear evolution equations (NLEEs) explain the physical problems in different branches of engineering and nonlinear science, for example, plasma physics, biology, fluid mechanics, optics, solid-state physics, etc. [1,2]
We have studied the nonlinear model depicting the wave proliferation in nonlinear low-pass electrical transmission lines (NLETLs) employing integration scheme modified Khater method
NLETLs have been discussed by the Lie analysis approach
Summary
The nonlinear evolution equations (NLEEs) explain the physical problems in different branches of engineering and nonlinear science, for example, plasma physics, biology, fluid mechanics, optics, solid-state physics, etc. [1,2]. We are using the MKM, which has not been used previously for this model Using this useful method on our supposed equation, we find some new kinds of wave patterns which are fruitful and very interesting results. We explore the wave solutions with the help of the integration technique, namely the modified Khater method [58,59], to solve the NLPDEs depicting the wave proliferation in the NLETLs. By using the translational vectors and their linear combinations, the NLETLs are converted to an equation wave proliferation in ordinary differential equation NLETLs. MKM is employed to find some new trigonometric and hyperbolic results which represent the consistency by Maple. Conservation laws play a very important role in constructing the analytical results of different types of nonlinear physical models.
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