The relation between a 2D Lotka-Volterra equation and a 2D Toda lattice

It is shown that the 2-discrete dimensional Lotka-Volterra lattice, the two dmensional Toda lattice equation and the recent 2-discrete dimensional Toda lattice equation of Santini et al can be obtained from a 2-discrete 2-continuous dimensional Lotka-Volterra lattice

A bilinear approach to a Pfaffian self-dual Yang-Mills equation

By using the bilinear technique of soliton theory, a pfaffian version of the SU(2) self-dual Yang-Mills equation and its solution is constructed

A direct approach to the ultradiscrete KdV equation with negative

A generalisation of the ultra-discrete KdV equation is investigated using a direct approach. We show that evolution through one time step serves to reveal the entire solitonic content of the system

On A Superfield Extension of The ADHM Construction and N=1 Super Instantons

We give a superfield extension of the ADHM construction for the Euclidean theory obtained by Wick rotation from the Lorentzian four dimensional N=1 super Yang-Mills theory. In particular, we investigate the procedure to guarantee the Wess-Zumino gauge for the superfields obtained by the extended ADHM construction, and show that the known super instanton configurations are correctly obtained.Comment: 22 pages, LaTeX, v2: typos corrected, references adde

Generalizing the KP hierarchies: Pfaffian hierarchies

We derive the Pfaffian analogues of the equations in the single-component KP hierarchies and the modified KP hierarchies and present an example of a system derived by reduction of some of the equations in these Pfaffianized hierarchies

Pfaffianization of the Davey-Stewartson equations

We use the bilinear method from soliton theory to produce a Pfaffian version of the Davey–Stewartson equations. The solutions of this new system of equations are Pfaffians

Pfaffianization of the discrete KP equation

We use the procedure of Ohta and Hirota to generate an integrable, coupled system of discrete equations from the discrete KP equation

On a direct approach to quasideterminant solutions of a noncommutative modified KP equation

A noncommutative version of the modified KP equation and a family of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux transformations and the solutions are verified directly. We also verify directly an explicit connection between quasideterminant solutions of the noncommutative mKP equation and the noncommutative KP equation arising from the Miura transformation

On multiple soliton solutions of some simple differential-difference equations

Two integrable differential-difference equations introduced recently by Hu and Tam are examined. They are shown to come from reductions of the (modified) KP hierarchy. Multiple soliton solutions are presented

Two integrable differential-difference equations derived from the discrete BKP equation and their related equations

In this paper, two integrable differential-difference equations derived from the discrete BKP equation and their related equations are studied. The corresponding bilinear Bäcklund transformations (BTs) are presented. Starting from the bilinear BTs, soliton solutions of these equations are generated and the corresponding Lax pairs are obtained