  Using perturbative methods, we analyse a nonlinear generalisation of
Schrodinger's equation that had previously been obtained through
information-theoretic arguments. We obtain analytical expressions for the
leading correction, in terms of the nonlinearity scale, to the energy
eigenvalues of the linear Schrodinger equation in the presence of an external
potential and observe some generic features. In one space dimension these are:
(i) For nodeless ground states, the energy shifts are subleading in the
nonlinearity parameter compared to the shifts for the excited states, (ii) the
shifts for the excited states are due predominantly to contribution from the
nodes of the unperturbed wavefunctions and (iii) the energy shifts for excited
states are positive for small values of a regulating parameter and negative at
large values, vanishing at a universal critical value that is not manifest in
the equation. Some of these features hold true for higher dimensional problems.
We also study two exactly solved nonlinear Schrodinger equations so as to
contrast our observations. Finally, we comment on the possible significance of
our results if the nonlinearity is physically realised.
