On the Toda Lattice Equation with Self-Consistent Sources
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
The Toda lattice hierarchy with self-consistent sources and their Lax representation are derived. We construct a forward Darboux transformation (FDT) with arbitrary functions of time and a generalized forward Darboux transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS), which can serve as a non-auto-Backlund transformation between TLSCS with different degrees of sources. With the help of such DT, we can construct many type of solutions to TLSCS, such as rational solution, solitons, positons, negetons, and soliton-positons, soliton-negatons, positon-negatons etc., and study properties and interactions of these solutions.
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Cite
@article{arxiv.nlin/0510014,
title = {On the Toda Lattice Equation with Self-Consistent Sources},
author = {Xiaojun Liu and Yunbo Zeng},
journal= {arXiv preprint arXiv:nlin/0510014},
year = {2007}
}
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20 pages