![]() NLPDEs have recently become quite popular in various topics such as optical fiber, fractional dynamics, fluid mechanics, control theory, chemical kinematics, signal transmission control theory, plasma physics, earthquakes, relativistic, solid-state physics, chemical physics, geochemistry, ecosystem, biomechanics, biophysics, gas dynamics, and so forth. The usefulness of explicit traveling wave solutions for nonlinear partial differential equations (NLPDEs) is noteworthy in the current situation. In nonlinear engineering, physics, and mathematics, solving the nonlinear models would still be a useful approach for comprehending the complicated systems. Hence, the presented methods are relatable and efficient to solve nonlinear problems in mathematical physics. After the successful implementation of the presented methods, the exact solitary wave solutions in the form of trigonometric, rational, and hyperbolic functions are obtained. The nonlinear ordinary transform to concern the generalized Schrodinger equation to convert it for a solvable integer-order differential equation is used. The techniques are the improved function method and the improved simple equation method. The novel analytical wave solutions to the mentioned nonlinear equation in the sense of the nonlinear ordinary differential transform equation are obtained. Here, the miscellaneous soliton solutions of the generalized nonlinear Schrödinger equation are considered that describe the model of few-cycle pulse propagation in metamaterials with parabolic law of nonlinearity.
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