Reality problems in the soliton theory
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
This is a survey article dedicated mostly to the theory of real regular "finite-gap" (algebro-geometrical) periodic and quasiperiodic Sine-Gordon solutions. Long period this theory remained unfinished and ineffective, and by that reason practically had no applications. Even for such simple physical quantity as "Topological Charge" no formulas existed expressing it through the "Inverse Spectral Data". Few years ago the present authors solved this problem and made this theory effective. This article contains description of the history and recent achievements. It describes also the reality problems for several other fundamental soliton systems.
Keywords
Cite
@article{arxiv.nlin/0609063,
title = {Reality problems in the soliton theory},
author = {P. G. Grinvich and S. P. Novikov},
journal= {arXiv preprint arXiv:nlin/0609063},
year = {2007}
}
Comments
LaTeX, 19 pages, 3 figures