Abstract. We study the integrable systems in higher dimensions which can be written not by the Hirota's bilinear form but by the trilinear form. We explicitly discuss about the Bogoyavlenskii-Schiff(BS) equation in (2 + 1) dimensions. Its analytical proof of multi soliton solution and a new feature are given. Being guided by the strong symmetry, we also propose a new equation in (3 + 1) dimensions.
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We discuss an analytic proof of a conjecture (Nakamura) that solutions of Toda molecule equation give those of Ernst equation giving Tomimatsu-Sato solutions of Einstein equation. Using Pfaffian identities it is shown for Weyl solutions completely and for generic cases partially.April 1995 Rits-TH-9511 TOHO-FP-9551
Multichannel sub-Nyquist sampling is an efficient technique to break through the limitation of the Nyquist sampling theorem for the wideband digital instantaneous frequency measurement (DIFM) receiver. The significant challenge is calculating the folding frequency and solving the ambiguity quickly and accurately. Usually, the researchers adopt a fast Fourier transform (FFT) to calculate the folding frequency and a Chinese remainder theorem (CRT) to solve the ambiguity caused by undersampling. However, these algorithms have the drawback of long response time. In this paper, we use a frequency deduction algorithm based on the total least-squares estimation to measure the folding frequency accurately within a few clocks. We propose a frequency-band division algorithm by dividing the measurable frequency range into a few sub-bands to solve the frequency ambiguity. This deblurring algorithm is more efficient and faster than CRT. We analyse the performance of our algorithms by numerical simulations and functional hardware simulations and compare them with FFT and CRT. We also conduct experiments on a hardware platform to confirm the effectiveness of our algorithms. The simulation results show that our algorithms have better performance than FFT and CRT in accuracy and response time. Board-level measurement results verify that the proposed DIFM technique can capture the frequency from 0 to 5,000 MHz with a maximum of 0.8 MHz root-mean-squared error in less than 200 ns.
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