Accelerating Airy beams in the presence of inhomogeneities

•Novel accelerating Airy beam solutions have been obtained in the presence of five types of inhomogeneities.•An inverted harmonic oscillator (diverging parabolic GRIN profile).•A linearly forced inverted harmonic oscillator.•A hyperbolic secant well.•A guided quartic potential.•A position-dependent mass (PDM) isospectral system.

Studies have already been made of accelerating Airy beams in the presence of deterministic inhomogeneities, illustrating, in particular, that the inherent self-healing properties of such beams are preserved. The cases of a range-dependent linear transverse potential and a converging GRIN structure (harmonic oscillator) have been examined thoroughly. Examples will be given in this article of novel accelerating Airy beams in the presence of five other types of potential functions. Three of the resulting exact analytical solutions have a common salient characteristic property: they are constructed using the free-space accelerating Airy beam solution as a seed.