Asymptotic Expansions and Amplification of a Gravitational Lens Near a
  Fold Caustic
  We propose two methods that enable us to obtain approximate solutions of the
lens equation near a fold caustic with an arbitrary degree of accuracy. We
obtain "post-linear" corrections to the well-known formula in the linear
caustic approximation for the total amplification of two critical images of a
point source. In this case, in order to obtain the nontrivial corrections we
had to go beyond the approximation orders earlier used by Keeton et al. and to
take into account the Taylor expansion of the lens equation near caustic up to
the fourth order. Corresponding analytical expressions are derived for the
amplification in cases of the Gaussian and power-law extended source models;
the amplifications depend on three additional fitting parameters. Conditions of
neglecting the correction terms are analysed. The modified formula for the
amplification is applied to the fitting of light curves of the Q2237+0305
gravitational lens system in a vicinity of the high amplification events
(HAEs). We show that the introduction of some "post-linear" corrections reduces
chi^2 by 30% in the case of known HAE on the light curve of image C (1999).
These corrections can be important for a precise comparison of different source
models with regard for observational data. Key words: gravitational lensing:
micro - quasars: individual (Q2237+0305) - gravitational lensing: strong -
methods: analytical
