Nonlinearity from Linearity: the Ermakov-Piney Equation Revisited
In this short note we revisit the so-called Ermakov-Pinney (EP)
equation viewing its properties from a physically motivated
perspective. We discuss its ties with the Schrodinger equation
from such a perspective, demonstrating how the Ermakov-Pinney equation arises
essentially due to the conservation of angular momentum.
One of the main findings of the present work is how to use this
conservation law to give a simple geometric proof of
the nonlinear superposition principle applicable to the solutions of the
EP equation. We also present ways in which the EP equation can be
generalized and discuss their connections to earlier work.
The other main novelty of this work consists of the generalization
of the EP equation to higher dimensions.
KEVREKIDIS Panayotis;
DROSSINOS Ioannis;
2007-03-29
ELSEVIER SCIENCE BV
JRC34783
https://publications.jrc.ec.europa.eu/repository/handle/JRC34783,
10.1016/j.matcom.2006.10.005,
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