Modified Emden and the corresponding standard PDM dynamical equations: exact solvability and classicalstates crossings
Abstract
We introduce the positiondependent mass (PDM) settings for the modified Emden equation (MEE). To work out exact solutions for the PDMMEE, we use the most general solution for the simple harmonic oscillator's dynamical equation (i.e., the initial conditions shall be identified by the PDMMEE problem at hand) and report the most general solution for the MEE. In so doing, we use a nonlocal point transformation. Next, we map MEEsolution into the corresponding PDMMEE. Two PDMMEEtype classical particles are used as illustrative examples, and their exact solutions are reported. Under specific parametric considerations, the phasespace trajectories are observed to have classicalstates crossings as they evolve in time (where each phasespace trajectory represents a classical state). This observation holds true not only for PDMMEEtype classical particles but also for MEEtype particles.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.13758
 Bibcode:
 2021arXiv210713758M
 Keywords:

 Physics  Classical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 12 pages, 19 figures