Results 1 - 10 of 292
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[en] By solving the normalized dimensionless linear Schrödinger-like equation with harmonic potential analytically, we have studied the spatiotemporal Airy Gaussian (AiG) and Airy Gaussian vortex (AiGV) light bullets. The AiG light bullets are composed of the chirped Airy functions in temporal domain and the AiG functions in spatial domain, while AiGV light bullets are AiG light bullets carrying the vortex. By selecting the negative or positive linear chirp we can obtain decelerating or accelerating light bullets, respectively. Combing effects from harmonic potential with the negative quadratic chirp, we can study reversed light bullets in both spatial and temporal domains. (letter)
[en] We consider the asymptotic expansion of the logarithmic derivative of the Airy function Ai'(z)/Ai(z), and also its reciprocal Ai(z)/Ai'(z), as |z| → ∞. We derive simple, closed-form solutions for the coefficients which appear in these expansions, which are of interest since they are encountered in a wide variety of problems. The solutions are presented as Mellin transforms of given functions; this fact, together with the methods employed, suggests further avenues for research.
[en] Integral representations are obtained for some quartic products of the Airy functions Ai(z) and Bi(z). These integral representations are particularly useful in obtaining the constants which appear in the asymptotic expansions of their integrals. Some of these results are also relevant to the connection problem for the second Painlevé transcendent.
[en] The decay mode solutions for the Kadomtsev-Petviashvili (KP) equation are derived by Hirota method (direct method). The decay mode solution is a new set of analytical solutions with Airy function. (general)
[en] Integral representations are derived for the Riesz fractional derivatives of the product of two functions, Dxα(uv). Here u(x)=∫∞-∞Ai(x- y)f(y) dy and v(x)=∫∞-∞Ai(x-y)g(y) dy are the Airy transforms of the functions f(x) and g(x), respectively, and Ai(x) is the Airy function of the first kind. This derivation is based on the new Hankel transform-type formula for Ai(x-a)Ai(x-b), where a, binR. Estimates of Dxα(uv) in L∞(R) are obtained. They can be used for the study of small data scattering for the Korteweg-de Vries-type equations.
[en] In this short paper we derive a formula for the spatial persistence probability of the Airy1 and the Airy2 processes. We then determine numerically a persistence coefficient for the Airy1 process and its dependence on the threshold. (paper)
[en] Several recent works have considered the pressure exerted on a wall by a model polymer. We extend this consideration to vesicles attached to a wall, and hence include osmotic pressure. We do this by considering a two-dimensional directed model, namely that of area-weighted Dyck paths. Not surprisingly, the pressure exerted by the vesicle on the wall depends on the osmotic pressure inside, especially its sign. Here, we discuss the scaling of this pressure in the different regimes, paying particular attention to the crossover between positive and negative osmotic pressure. In our directed model, there exists an underlying Airy function scaling form, from which we extract the dependence of the bulk pressure on small osmotic pressures. (paper)
[en] Integral representations are obtained for some cubic products of the Airy functions Ai(z) and Bi(z). These integral representations are of the Laplace contour type but they involve the modified Bessel functions of order . From these results it is then possible to evaluate a number of definite integrals involving such cubic products.
[en] Spatiotemporal controllable accelerating and decelerating Airy–Airy-vortex (CAiAiV) light bullets are obtained by solving the dimensional free space Schrödinger equation. For these light bullets, the temporal parts come from controllable Airy distributions, and the spatial parts come from controllable Airy vortex distributions. Their propagation properties are affected by the initial velocity, the topological charge and the decay factor. A positive initial velocity causes self-acceleration in both the spatial and the temporal domains of the CAiAiV light bullet, while negative initial velocity makes it first decelerate and then accelerate. The maximum decelerating deflection is determined by the negative initial velocity. The structure of CAiAiV light bullets is influenced by weakening the main lobe and strengthening the side lobes with the topological charge increasing. The peculiar propagation properties of the side lobes of such light bullets are also affected by the decay factors in X, Y and T directions. The superposition of different-order CAiAiV functions is also discussed. (letter)