Dressing method and the coupled KP hierarchy

The coupled KP hierarchy, introduced by Hirota and Ohta, are investigated by using the dressing method. It is shown that the coupled KP hierarchy can be reformulated as a reduced case of the 2-component KP hierarchy.Comment: 11 pages, LaTeX, no figure

Bilinearization of Discrete Soliton Equations and Singularity Confinement

Bilinear forms for some nonlinear partial difference equations(discrete soliton equations) are derived based on the results of singularity confinement. Using the bilinear forms, the N-soliton and algebraic solutions of the discrete potential mKdV equation are constructed.Comment: 14 pages, LaTe

Constructing a Supersymmetric Integrable System from the Hirota Method in Superspace

An N=1 supersymmetric system is constructed and its integrability is shown by obtaining three soliton solutions for it using the supersymmetric version of Hirota's direct method.Comment: 10 pages, no figure

Complexiton Solutions of the Toda Lattice Equation

A set of coupled conditions consisting of differential-difference equations is presented for Casorati determinants to solve the Toda lattice equation. One class of the resulting conditions leads to an approach for constructing complexiton solutions to the Toda lattice equation through the Casoratian formulation. An analysis is made for solving the resulting system of differential-difference equations, thereby providing the general solution yielding eigenfunctions required for forming complexitons. Moreover, a feasible way is presented to compute the required eigenfunctions, along with examples of real complexitons of lower order.Comment: 21 pages, Latex, to appear in Physica