In this paper a higher order non–linear differential equation is given and it becomes a higher order Airy equation (in our terminology) under the Cole–Hopf transformation. For the even case a solution is explicitly constructed, which is a generalization of the Airy function. We start with an example to state our motivation. For the simple non–linear equation of Riccati type y + y = x (1) with a...

1 Correction to the Airy Approximation In Ref..1] and especially in Franz and Galle 2] one can nd correction terms to order O((ka) ?5=3) to the standard Airy approximation of the zeros l of the Hankel function H (1) (ka) in the complex-plane 1 : l = ka + e ii=3 (ka)

We systematically characterize the Fabry-Pérot resonator. We derive the generic Airy distribution of a Fabry-Pérot resonator, which equals the internal resonance enhancement factor, and show that all related Airy distributions are obtained by simple scaling factors. We analyze the textbook approaches to the Fabry-Pérot resonator and point out various misconceptions. We verify that the sum of th...

For a simple Lie algebra g we define a system of linear ODEs with polynomial coefficients, which we call the topological equation of g-type. The dimension of the space of solutions regular at infinity is equal to the rank of the Lie algebra. For the simplest example g = sl2(C) the regular solution can be expressed via products of Airy functions and their derivatives; this matrix valued function...

The Debye series is developed for electromagnetic scattering by a spheroid in order to decompose the far-zone fields into various physical processes. The geometrical rainbow angle and supernumerary spacing parameter are determined from the Debye intensity by fitting the results to an Airy function and comparing them to their assumed values in ray optics and Airy theory, respectively. Eccentrici...

We show that a weak Airy pulse can be used to manipulate the dynamics of an optical soliton when propagating at a different wavelength. Our results indicate that an Airy wave packet is considerably more effective in controlling the arrival time of a soliton than a corresponding Gaussian pulse. The nature of these interactions is systematically explored as a function of the initial parameters us...