Nonlinear supersymmetric (Darboux) covariance of the ErmakovMilnePinney equation
Abstract
It is shown that the nonlinear ErmakovMilnePinney equation ρ″+ v( x) ρ= a/ ρ^{3} obeys the property of covariance under a class of transformations of its coefficient function. This property is derived by using supersymmetric, or Darboux, transformations. The general solution of the transformed equation is expressed in terms of the solution of the original one. Both iterations of these transformations and irreducible transformations of second order in derivatives are considered to obtain the chain of mutually related ErmakovMilnePinney equations. The behaviour of the Lewis invariant and the quantum number function for bound states is investigated. This construction is illustrated by the simple example of an infinite square well.
 Publication:

Physics Letters A
 Pub Date:
 May 2003
 DOI:
 10.1016/S03759601(03)00495X
 arXiv:
 arXiv:mathph/0209013
 Bibcode:
 2003PhLA..311..200I
 Keywords:

 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 8 pages