Solving the (2+1)-Dimensional Derivative Toda Equation

Five-Dimensional Gauge Theories and Whitham-Toda Equation

The five-dimensional supersymmetric SU(N) gauge theory is studied in the framework of the relativistic Toda chain. This equation can be embedded in two-dimensional Toda lattice hierarchy. This system has the conjugate structure. This conjugate structure corresponds to the charge conjugation.

Solving Two-Dimensional Fuzzy Partial Dierential Equation by the Alternating Direction Implicit Method

Replica limit of the toda lattice equation.

In a recent breakthrough Kanzieper showed that it is possible to obtain exact nonperturbative random matrix results from the replica limit of the corresponding Painlevé equation. In this article we analyze the replica limit of the Toda lattice equation and obtain exact expressions for the two-point function of the Gaussian unitary ensemble and the resolvent of the chiral unitary ensemble. In th...

Direct “delay” Reductions of the Toda Equation

A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differentialdifference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classic...

q-Discrete Toda Molecule Equation

A q-discrete version of the two-dimensional Toda molecule equation is proposed through the direct method. Its solution, Bäcklund transformation and Lax pair are discussed. The reduction to the q-discrete cylindrical Toda molecule equation is also discussed. 1 On leave from Department of Applied Mathematics, Faculty of Engineering, Hiroshima University. 1