Complexiton Solutions of the Toda Lattice Equation

Details Complexiton Solutions of the Toda Lattice Equation Complexiton Solutions of the Toda Lattice Equation

2004-06-08

arxiv.org/abs/nlin/0406014v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

21 pages, Latex, to appear in Physica A

Scientific paper

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.

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