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In this work, the tanh method is employed to compute some traveling wave patterns of the nonlinear third-order (2+1) dimensional Chaffee-Infante (CI) equation. The tanh technique is successfully used to get the traveling wave solutions of a considered model in the form of some hyperbolic functions. The Lie symmetry technique is used to analyze the Chaffee-Infante (CI) equation and compute the Infinitesimal generators under the invariance criteria of Lie groups. Then we construct the commutator table, adjoint representation table, and we have represented symmetry groups for each Infinitesimal generator. The optimal system and similarity reduction method is used to obtain some analytical solutions of the considered model. With the help of the similarity reduction method, we have converted the nonlinear partial differential equation into nonlinear ordinary differential equations (ODEs). Moreover, we have shown graphically obtained wave solutions by using the different values of involving parameters. Conserved quantities of nonlinear CI equation are obtained by the multiplier approach.

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The nonlinear transmission line (NLTL) equations are significant nonlinear evolution equations (NLEEs) in nonlinear electrical transmission line (NLETL) regulation. The tanh 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.