On purely nonlinear oscillators generalizing an isotonic potential.

Abstract (1) We consider a nonlinear generalization of the isotonic oscillator with an asymmetric potential. (2) Using a symmetrization principle we construct a symmetric potential. (3) The period function in this potential has the same value as in the original asymmetric potential. (4) It is amplitude dependent and expressible in terms of the hypergeometric function. Highlights • An exact analytical formula for the time period is calculated which reduces to that of the linear harmonic oscillator for the appropriate value of the relevant parameter. • A symmetrization argument is used to transform the potential such that the time period in the transformed symmetric potential matches that in the original asymmetric potential. [ABSTRACT FROM AUTHOR]