Position-dependent Mass Lagrangians: Nonlocal Transformations, Euler-Lagrange Invariance and Exact Solvability

This thesis reviews some features of the PDM Lagrangians. We reach the mapping of the PDM equation into a unit-mass Lagrangian in the generalized coordinates by the insertion of a nonlocal point transformation. The invariance of the PDM Euler-Lagrange equations under specific conditions is proved. We analyze the dynamical equations obeyed by nonlinear oscillator systems with position-dependent mass. Four classes of such examples with PDM-nonlinear oscillators are specified. They include Mathews-Lakshmanan oscillators, a quadratic nonlinear oscillator, a Morse-type oscillator, and a nonlinear deformation of an isotonic oscillator. Attainment among them the mapping of an isotonic nonlinear oscillator into a PDM deformed isotonic oscillator. Keywords: classical position-dependent mass, nonlocal point transformation, Euler-Lagrange equations invariance.