  This work aims to explain the amplification of curvature perturbations on
small scales arising from the phenomenon of self-resonance. By making a series
expansion of the inflationary potential and employing perturbative techniques
to solve for the inflaton field, we reformulate the Mukhanov-Sasaki equation
into a Hill equation. Then, we derive expressions for the Floquet exponents
corresponding to a potential having both cubic and quartic terms in its
expansion. Our analytical results are then compared with numerical
computations. Moreover, we propose potential applications including the
generation of Primordial Black Holes, Scalar-Induced Gravitational Waves, and
Oscillons.
