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The low-pass nonlinear electrical transmission lines and the Cahn-Allen equation are important nonlinear model equations to figure out different tangible systems, namely, electrical engineering, fluid dynamics etc. The contrivance of this study is to introduce advanced Bernoulli sub-equation function method to search for stable and effective solitary solutions of the described wave equations. Stable solitary solutions are reported as an integration of exponential functions, hyperbolic functions, etc., and the graphical implications for specific values of the corresponding parameters are explained in the solutions obtained in order to uncover the inmost structure of the tangible phenomena. It is establish that the IBSEF method is reliable, contented and might be used in further works to found ample novel soliton solutions for other types of NLEEs arising in physical science and engineering.