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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...

Airy beams are non-diffracting optical beams first predicted by Berry and Balazs in 1979 and first demonstrated experimentally by Siviloglou, Broky, Dogariu, and Christodoulides in 2007. What makes an Airy beam unique is that it can be created in one dimension and that its lobe of highest intensity propagates along a parabolic path. Airy beams can be used for a variety of purposes including par...

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 consider a discrete polynuclear growth (PNG) process and prove a functional limit theorem for its convergence to the Airy process. This generalizes previous results by Prähofer and Spohn. The result enables us to express the F1 GOE Tracy-Widom distribution in terms of the Airy process. We also show some results, and give a conjecture, about the transversal fluctuations in a point to line las...

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...

We report the first observation of Airy optical beams. This intriguing class of wave packets, initially predicted by Berry and Balazs in 1979, has been realized in both one- and two-dimensional configurations. As demonstrated in our experiments, these Airy beams can exhibit unusual features such as the ability to remain diffraction-free over long distances while they tend to freely accelerate d...

We report the experimental generation and dynamic trajectory control of plasmonic Airy beams (PABs). The PABs are created by directly coupling free-space Airy beams to surface plasmon polaritons through a grating coupler on a metal surface. We show that the ballistic motion of the PABs can be reconfigured in real time by either a computer addressed spatial light modulator or mechanical means.

In this paper, we establish the linear profile decomposition for the Airy equation with complex or real initial data in L, respectively. As an application, we obtain a dichotomy result on the existence of maximizers for the symmetric Airy-Strichartz inequality.

We report experiments and numerical simulations on the self-focusing and filamentation of ultraintense femtosecond Airy waveforms in water. The accelerating property of Airy waveforms results in the generation of distinct features in the angularly resolved spectra of forward-propagating supercontinuum emission. Fitting these features with appropriate phase-matching conditions allows for the qua...