Reality problems in the soliton theory

Details Reality problems in the soliton theory Reality problems in the soliton theory

2006-09-27

arxiv.org/abs/nlin/0609063v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX, 19 pages, 3 figures

Scientific paper

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.

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