Accessing Levinson-Smith and Li' e nard equations in a nonlinear framework of quantum mechanics

In this paper, we present the reduction of a recently introduced generalized quantum scheme of Chodos and Cooper to Levinson-Smith and Liénard classes of nonlinear system that enable us to furnish a wider class of acceptable solutions. In particular, for the Levinson-Smith equations, we find their relevance to position-dependent mass quantum systems, with an interesting off-shoot that solitonic-like solutions emerge from the condition of the level surface in the system. On the other hand, for the Liénard type, which has coefficients of odd and odd symmetry in the present set up, we demonstrate that closed form solutions exist on carrying out conversion to the typical Abel form.