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Tetsu Yajima

Publications and source records attributed to Tetsu Yajima.

12 recordsLinked to original sources
arXiv2017

An Approximation Method for the Scattering Data of One-Dimensional Soliton Equations under Arbitrary Rapidly-Decreasing Initial Pulses

We present a novel approximation method that can predict the number of solitons asymptotically appearing under arbitrary rapidly decreasing initial wave packets. The number of solitons can be estimated without integration of the original soliton equations. As an example, we take the one-dimensional nonlinear Schrodinger equation and estimate the behaviors of the scattering amplitude in detail. The results show good agreement compared with those obtained by direct numerical integration. The presented method is applicable to a wide class of one-dimensional soliton equations.

nlin.SI↗
arXiv2015

A CA Hybrid of the Slow-to-Start and the Optimal Velocity Models and its Flow-Density Relation

The s2s-OVCA is a cellular automaton (CA) hybrid of the optimal velocity (OV) model and the slow-to-start (s2s) model, which is introduced in the framework of the ultradiscretization method. Inverse ultradiscretization as well as the time continuous limit, which lead the s2s-OVCA to an integral-differential equation, are presented. Several traffic phases such as a free flow as well as slow flows corresponding to multiple metastable states are observed in the flow-density relations of the s2s-OVCA. Based on the properties of the stationary flow of the s2s-OVCA, the formulas for the flow-density relations are derived.

nlin.CG↗
arXiv2015

Roles of Interfering Radiation Emitted from Decaying Pulses Obeying Soliton Equations Belonging to the Ablowitz-Kaup-Newell-Segur Systems

The nonlinear Schrodinger (NLS) equation under the box-type initial condition, which models general multiple pulses deviating from pure solitons, is analyzed. Following the approximation by splitting the initial pulse into many small bins [G. Boffetta and A. R. Osborne, J. Comp. Phys. 102, 25 (1992)], we can analyze the Zakharov-Shabat eigenvalue problem to construct transfer matrices connecting the Jost functions in each interval without direct numerical computation. We can obtain analytical expressions for the scattering data that describe interfering radiation emitted from initial pulses. The number of solitons that appear in the final stage is predicted theoretically, and the condition generating an unusual wave such as a double-pole soliton is derived. Numerical analyses under box-type initial conditions are also performed to show that the interplay between the tails from decaying pulses can affect the asymptotic profile.

nlin.SI↗
arXiv2014

Amended Proof of Pitaevskii-Stringari's Theorem

An amended proof of Pitaevskii-Stringari's theorem is given in mathematically coherent manner without resorting to the Bogoliubov approximation. This approach is based on the orthodox quantum field theory which rigorously maintains the canonical commutation relations. Moreover, we make a sound argument by taking the thermodynamic limit which the authors of the original papers did not refer to. We conclude that there is no Bose Einstein Condensation (BEC) as a phase transition based on the Spontaneous Symmetry Breaking (SSB) of the global $U(1)$ gauge symmetry in flat one dimensional geometry even absolute zero temperature.

cond-mat.quant-gas↗
arXiv2014

Perturbative Analysis of Potential Scattering Problems in the Lieb-Liniger Model

The Lieb-Liniger model which has a weak external potential term under the periodic boundary condition is investigated. By exploiting the Bethe states as bases, we perform a perturbation analysis up to the first order to obtain the shifts of eigenenergies and corresponding eigenstates which have been brought about by the external potential. If we take a sufficiently large system, the eigenstates can be "the Schrödinger's cat states". Expectation values of the density operator taken between two Bethe states can be calculated with the aid of the Slavnov's formula and we evaluate the influence of the many-body interaction to the system under the external potential. The system is insensitive to the external potential because of the many-body interaction.

cond-mat.quant-gas↗
arXiv2012

Exact Solutions and Flow--Density Relations for a Cellular Automaton Variant of the Optimal Velocity Model with the Slow-to-Start Effect

A set of exact solutions for a cellular automaton, which is a hybrid of the optimal velocity and the slow-to-start models, is presented. The solutions allow coexistence of free flows and jamming or slow clusters, which is observed in asymptotic behaviors of numerically obtained spatio-temporal patterns. An exact expression of the flow--density relation given by the exact solutions of the model agrees with an empirical formula for numerically obtained flow--density relations.

nlin.CG↗
arXiv2012

Interference Pattern Formation between Bounded-Solitons and Radiation in Momentum Space: Possible Detection of Radiation from Bounded-Solitons with Bose-Einstein Condensate of Neutral Atoms

We propose an indirect method to observe radiation from an incomplete soliton with sufficiently large amplitude. We show that the radiation causes a notched structure on the envelope of the wave packet in the momentum space. The origin of this structure is a result of interference between the main body of oscillating solitons and the small radiation in the momentum space. We numerically integrate the nonlinear Schrödinger equation and perform Fourier transformation to confirm that the predicted structure really appears. We also show the simple model which reproduces the qualitative result. Experimental detection of the notched structure with Bose-Einstein condensation of neutral atoms is discussed and suitable parameters for this detection experiment are shown.

cond-mat.quant-gas↗
arXiv2011

Decay of Resonance Structure and Trapping Effect in Potential Scattering Problem of Self-Focusing Wave Packet

Potential scattering problems governed by the time-dependent Gross-Pitaevskii equation are investigated numerically for various values of coupling constants. The initial condition is assumed to have the Gaussian-type envelope, which differs from the soliton solution. The potential is chosen to be a box or well type. We estimate the dependences of reflectance and transmittance on the width of the potential and compare these results with those given by the stationary Schrödinger equation. We attribute the behaviors of these quantities to the limitation on the width of the nonlinear wave packet. The coupling constant and the width of the potential play an important role in the distribution of the waves appearing in the final state of scattering.

cond-mat.quant-gas↗
arXiv2008

Stochastic Process Associated with Traveling Wave Solutions of the Sine-Gordon Equation

Stochastic processes associated with traveling wave solutions of the sine-Gordon equation are presented. The structure of the forward Kolmogorov equation as a conservation law is essential in the construction and so is the traveling wave structure. The derived stochastic processes are analyzed numerically. An interpretation of the behaviors of the stochastic processes is given in terms of the equation of motion.

nlin.SI↗
arXiv2005

Max-Plus Algebra for Complex Variables and Its Application to Discrete Fourier Transformation

A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number of complex variables. As an application, the max-plus transformation is applied to the discrete Fourier transformation. Stretched coordinates are introduced to obtain the max-plus transformation whose imaginary part coinsides with a phase of the discrete Fourier transformation.

nlin.SI↗
arXiv1995

Numerical Studies of Localized Structures on an Uneven Bottom in Two Dimensions

The Davey-Stewartson (DS) equations with a perturbation term are presented by taking a fluid system as an example on an uneven bottom. Stability of dromions, solutions of the DS equations with localized structures, against the perturbation is investigated numerically. Dromions decay exponentially under an effect of the perturbation, while they travel stably after the effect disappears. The decay ratio of dromions is found to have relation to velocities of dromions. The important role played by the mean flow, which acts as an external force to the system, is discussed. These results show that dromions are quite stable as a localized structure in two dimensions, and they are expected to observed in various physical systems such as fluid or plasma systems.

solv-int↗