The Hirota–Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota–Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge tran...

By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional KadomtsevPetviashvili (KP-II) equation is proposed. We show that dissipative solitons (dissipatons) of those members give rise to the real solitons of KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for KP-II, by whic...

presentation 1. Iiizumi M, Bandyopadhyay S, Hirota, S, Hosobe, S, Tsukada T, Miura K, Saito K, Watabe M, Furuta E, Zhan R, Pai S, Mohinta S and Watabe K. (Apr. 2006) Expression of RhoC correlates with metastatic disease and survival of prostate cancer patients American Association for Cancer Research. Washington DC 2. Bandyopadhyay, S., Zhan, Z., Wang, Y., Pai, SK., Hirota, S., Hosobe, S., Taka...

We introduce an extension of the l-reduced KP hierarchy, which we call the lBogoyavlensky hierarchy. Bogoyavlensky’s 2 + 1-dimensional extension of the KdV equation is the lowest equation of the hierarchy in case of l = 2. We present a group-theoretic characterization of this hierarchy on the basis of the 2-toroidal Lie algebra sl l . This reproduces essentially the same Hirota bilinear equatio...

Scarf (1960) proposed a market environment and a model of dynamic adjustment in .which the standard tatonnement price adjustment process orbits around, rather than converges to, the competitive equilibrium. Hirota ( 1981) characterized the price paths by the configuration of endowments. We explore the predictions of Scarf's model in a non­ tatonnement experimental double auction. We find that t...

We introduce an extension of the l-reduced KP hierarchy, which we call the lBogoyavlensky hierarchy. Bogoyavlensky’s 2 + 1-dimensional extension of the KdV equation is the lowest equation of the hierarchy in case of l = 2. We present a group-theoretic characterization of this hierarchy on the basis of the 2-toroidal Lie algebra sl l . This reproduces essentially the same Hirota bilinear equatio...

The Hirota equation is a modified nonlinear Schrödinger equation (NLSE) that takes into account higher-order dispersion and time-delay corrections to the cubic nonlinearity. In describing wave propagation in the ocean and optical fibers, it can be viewed as an approximation which is more accurate than the NLSE. We have modified the Darboux transformation technique to show how to construct the h...

Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. A theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the Deformatio...

In this paper, we establish exact solutions for the timefractional Klein-Gordon equation, and the time-fractional HirotaSatsuma coupled KdV system. The Hes semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply Hes semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the timefractional Hirota...