4Department of Pharmaceutical Engineering, Faculty of Engineering, Toyama Prefectural University, Kurokawa, Imizu, Toyama 939-0398, Japan 5Department of Hygienic Sciences, Kobe Pharmaceutical University, 4-19-1 Motoyamakita-machi, Higashinada-ku, Kobe 658-8558, Japan *Corresponding authors: Yoshihisa Hirota, Laboratory of Biochemistry, Department of Bioscience and Engineering, College of System...

Who remembers 'Hirota's method'? In the early days of solitons, although the Korteweg-de Vries equation had been solved by the 'inverse scattering method' most solutions to integrable non-linear equations were found by simpler more direct methods. Outstanding among these was a method due mainly to Hirota, which involved casting the equation into a 'bilinear form' and then applying intelligent g...

We discretise the Lax pair for reduced Nahm systems and prove its equivalence with Kahan–Hirota–Kimura discretisation procedure. show that these pairs guarantee integrability of discrete providing an invariant. Also, we cannot solve general problem characterisation discretisations.

In this paper, the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation is investigated to acquire complexiton solutions by Hirota direct method. It essential transform into bi-linear form and build N-compilexiton pairs of conjugate wave variables.

A resonance between long and short waves will occur if the phase velocity of the long wave matches the group velocity of the short wave. In this paper, a system with two distinct packets of short waves in resonance with a common long wave is studied. Breather solutions are calculated by the Hirota bilinear method, and rogue wave modes (unexpectedly large displacements from an otherwise calm bac...

For the Kac-Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra D (1) n , we compute the coefficients of the corresponding Hirota bilinear equations, and verify the coincidence of these bilinear equations with the ones that are satisfied by Givental’s total descendant potential of the Dn singularity, as conjectured ...

Interest to the tasks by bound with systems of the quasilinear equations recently has revived. Therefore we have decided to expose in electronic sort our operation published in Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 2, pp. 189-199, November, 1994. Original article submitted October 26, 1993. Exact single-wave and two-wave solutions of systems of equations of th...

We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the non-commutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the three-dimensional consistency property remains valid in this case. We derive the non-commutative zero curvature representations for these systems, based on the latter proper...

It is shown that symplectic and orthogonal Schur functions can be realized by the action of the modes of certain vertex operators on the function 1. The properties of these vertex operators allow one to reproduce the basic propreties of these types of symmetric functions. The vertex operator modes are shown to obey free fermionic relations which provides applications such as calculating product...

Right This dissertation is author version of following the journal article. Yu Liu, Hiroaki Higashitsuji, Hisako Higashitsuji, Katsuhiko Itoh, Toshiharu Sakurai, Kazuhiko Koike, Kiichi Hirota, Manabu Fukumoto, Jun Fujita, Overexpression of gankyrin in mouse hepatocytes induces hemangioma by suppressing factor inhibiting hypoxia-inducible factor-1 (FIH1) and activating hypoxia-inducible factor-1...