Narimasa Sasa

N soliton solutions to the Bogoyavlenskii-Schiff equation and a quest for the soliton solution in (3 1) dimensions

We study the integrable systems in higher dimensions which can be written by the trilinear form instead of by the Hirotas bilinear form. We explicitly discuss the Bogoyavlenskii-Schiff equation in (2 + 1) dimensions. Its analytical proof of multisoliton solution and a new feature are given. Being guided by the strong symmetry, we also propose a new equation in (3 + 1) dimensions.

Three-dimensional dynamics of vortex-lattice formation in Bose-Einstein condensates

We numerically study the dynamics of vortex lattice formation in a rotating cigar-shaped Bose-Einstein condensate. The study is a three-dimensional simulation of the Gross-Pitaevskii equation with a phenomenological dissipation term. The simulations reveal previously unknown dynamical features of the vortex nucleation process, in which the condensate undergoes a strongly turbulent stage and the penetrating vortex lines vibrate rapidly. The vibrations arise from spontaneous excitation of Kelvin waves on the protovortices during a surface wave instability, caused by an inhomogeneity of the condensate density along the elongated axial direction.

Theory and Simulation of Electromagnetic Wave Emission from Intrinsic Josephson Junctions

Concerning the spontaneous THz electromagnetic wave emission from intrinsic Josephson junctions, we revisit the theory for intrinsic Josephson effects from standpoints of the couplings between stacked junctions and consequent superconducting phase dynamics. After reviewing the previous simulation works based on the theory, we present recent multi-physics simulation studies suggested by authors to systematically reproduce the emission experiments. Some typical simulation results are exhibited and the future perspective of the simulation is also given.

Neugebauer-Kramer solutions of the Ernst equation in Hirota's direct method

We prove analytically the Sasa-Satsuma conjecture which states that their solution of bilinear form of the Ernst equation gives the Neugebauere-Kramer solution in particular cases. This proof relates Hirotas direct method with the Backlund transformation method and opens the way towards the comprehensive interpretation of the Ernst equation.

Quadruple-Precision BLAS Using Bailey's Arithmetic with FMA Instruction: Its Performance and Applications

When a floating-point arithmetic is executed on a processor unit, round-off and truncation errors occur every calculation. These errors cause a precision issue in a large simulation which requires a great number of calculations. Therefore, we have developed the quadruple-precision basic linear algebra subprograms (QPBLAS) based on Baileys double-double arithmetic. The multiplication operation of Baileys arithmetic is realized by 24 double-precision operations. When using an FMA (fused multiply-add) instruction, we can reduce the number of operations in about half. Therefore, we develop QPBLAS using the FMA instruction and evaluate its performance. The result shows that the QPBLAS using FMA is basically faster than QPBLAS. Moreover, when we replace QPBLAS of the quadruple-precision eigenvalue solver QPEigenK with QPBLAS using FMA, we can obtain about 1020% speedup.

Reduction of the self-dual Yang-Mills equations by Bessel and Legendre functions

Two integrable nonlinear equations are derived by dimensional reductions of the SU(2) self-dual Yang-Mills equations. To derive the equations, we use Hirotas method and some properties of special functions, namely those of the Bessel and Legendre functions. Solutions of these equations are represented in terms of Toeplitz determinants whose elements are a superposition of the special functions.