Abstract
This paper introduces the fractal form of the generalized nonlinear Schrödinger equation, newly named as the Biswas–Milovic model (BM). The BM equation theoretically explains the transmission of solitons for transatlantic and transcontinental distances utilizing optical fibers. The BM equation relating to Kerr law, parabolic law and nonlinearity quadratic law was studied using a variational approach for optical soliton solutions. Essential novel conditions are presented that guarantee the existence of the appropriate solitons. Besides, the physical action of the solution obtained was recorded in terms of 3D and contour plots for distinct parameters for the three different nonlinearities. This study shows the relevance and huge potential of the variational approach to the generalized nonlinear Schrödinger equation.