Takahito Arai

The atmospheric transparency measured with a LIDAR system at the Telescope Array experiment

An atmospheric transparency was measured using a LIDAR with a pulsed UV laser (355 nm) at the observation site of Telescope Array in Utah, USA. The measurement at night for two years in 2007–2009 revealed that the extinction coefficient by aerosol at the ground level is 0.033−0.012+0.016km−1 and the vertical aerosol optical depth at 5 km above the ground is 0.035−0.013+0.019. A model of the altitudinal aerosol distribution was built based on these measurements for the analysis of atmospheric attenuation of the fluorescence light generated by ultra high energy cosmic rays.

Resonant Interactions of Y-Periodic Soliton with Line Soliton and Algebraic Soliton: Solutions to the Davey-Stewartson I Equation

The exact solutions to the Davey-Stewartson I equation are analyzed to study the nature of the interactions between y -periodic soliton and line soliton and between y -periodic soliton and algebraic soliton. The interactions are classified into several types according to the phase shifts due to collisions. There are two types of singular interactions: one is the resonant interaction where two solitons interact so as to make one soliton and the other is the extremely long-range interaction where two solitons interchange each other infinitely apart. Detail behaviors of interactions are illustrated graphically.

Quasi-line soliton interactions of the Davey?Stewartson I equation: on the existence of long-range interaction between two quasi-line solitons through a periodic soliton

A periodic soliton is turned into a line soliton accordingly as a parameter point approaches to the boundary of the existing domain in the parameter space for a nonsingular periodic-soliton solution. We will call the periodic soliton with parameters of the neighborhood of the boundary a quasi-line soliton in this paper, which seems to be the line soliton. The interaction between two quasi-line solitons is the same as the interaction between two line solitons, except for very small parameter-sensitive regions. However, in such parameter regions, there are new long-range interactions between two quasi-line solitons through the periodic soliton as the messenger under some conditions, which cannot be described by the two-line-soliton solution.

Soliton Stability to the Davey-Stewartson: I. Equation by the Hirota Method.

The stability of soliton of the Davey-Stewartson I equation is discussed by the Hirota method. A close relation exists between the periodic soliton resonance and the soliton instability to the transverse disturbances. It is shown that the solutions of periodic soliton resonance describe the nonlinear stage of the instability.

On existence of a parameter-sensitive region: quasi-line soliton interactions of the Kadomtsev–Petviashvili I equation

A line-soliton solution can be regarded as the limiting solution with parameters on the boundary between regular and singular regimes in the parameter space of a periodic-soliton solution. We call the periodic soliton with parameters of the neighborhood of the boundary a quasi-line soliton. The solution with parameters on the intersection of the two boundaries, in the parameter space of the two-periodic-soliton solution on which each periodic soliton becomes the line soliton, corresponds to the two-line-soliton solution. On the way of the turning into the two-line-soliton solution from the two-periodic-soliton solution as a parameter point approaches to the intersection, there is a small parameter-sensitive region where the interaction between two quasi-line solitons undergoes a marked change to a small parameter under some conditions. In such a parameter-sensitive region, there is a new long-range interaction between two quasi-line solitons, which seems to be the long-range interaction between two line solitons through the periodic soliton as the messenger. We also show that an attractive interaction between a finite amplitude quasi-line soliton and infinitesimal one is possible.

On the Existence of Parameter-Sensitive Regions: Resonant Interaction between Finite-Amplitude and Infinitesimal Periodic Solitons in the Davey–Stewartson II Equation

There is a very small but finite amplitude periodic soliton (an infinitesimal periodic soliton) that interacts resonantly with a finite-amplitude periodic soliton under certain conditions. It is shown here that there are certain parameter-sensitive regions in the parameter space of the two-periodic-soliton solution where the interaction between the two periodic solitons undergoes a marked change to a small parameter change. Such regions exist near the intersections of two planes on which the conditions of a singular interaction are satisfied. The resonance between a finite-amplitude periodic soliton and an infinitesimal periodic soliton is shown to be responsible for the singular interactions with parameters in these parameter-sensitive regions.

Long-Range Interaction between Two Periodic Solitons through Growing-and-Decaying Mode in the Davey–Stewartson I Equation

where r is constant. One important feature of the solutions to the DS I equation is the reversion of the unstable wave train to its initial state. The analytical solution for the nonlinear evolution of a modulational unstable mode is given by the growing-and-decaying (GD) mode solution. This shows that an unstable mode grows exponentially in its early stage. After reaching a maximummodulation, the unstable mode vanishes with time to reproduce the initial unmodulated state. The DS equation has a periodic soliton solution, which represents the spatial structure of the inclined sequence of algebraic solitons in addition to the dark line soliton and algebraic soliton solutions. In previous studies, we investigated the interactions between two periodic solitons, and between the periodic soliton and other types of solitons. Note that there are two types of singular interaction: the resonant interaction, in which two solitons interact so as to generate a single soliton, and the extremely long-range interaction, in which two solitons interchange each other infinitely apart through the messenger soliton, which is similar to a periodic soliton. Recently, the interaction between a soliton and a GD mode has been investigated, and the existence of resonant interactions has been demonstrated. We reported that the existence of the periodic soliton changed the evolution of the modulational instability markedly, as if the soliton dominated the evolution of instability. These results suggest the possible existence of an interaction between two solitons through the GD mode. The purpose of the present note is to show that a long-range interaction exists between two parallel periodic solitons through the GD mode. Using the N-soliton solution of Satsuma and Ablowitz, the solution that describes the interaction between two periodic solitons, which have the same real part ð ; Þ and different imaginary parts ð 1; 1Þ and ð 2; 2Þ of complex wave numbers, is written as

On Recurrent Solutions as Imbricate Series of Rational Growing-and-Decaying Modes: Solutions to the Davey-Stewartson Equation

where p = ±1, r is a constant. Equation (1) with p = 1 and p = −1 are called the DS I and DS II equation, respectively. Although it is known that the spatially periodic solitons can be constructed by the imbricate series of the algebraic solitons, we feel it is to be pointed out that the recurrent solutions can be constructed by the imbricate series of solutions. So in this note, it is shown that the growing-and-decaying mode and the breather solution to the DS equation are constructed as imbricate series of rational growing-and-decaying modes. The growing-and-decaying mode solution is given by