DOI: https://doi.org/10.30970/jps.03.391
ORBIT STRUCTURE OF FINITE ZONE SECTOR OF TODA EQUATION AND EQUATION OF THE KdV (MKdV) TYPE
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Journal of Physical Studies 3(4), 391–398 (1999)
DOI: https://doi.org/10.30970/jps.03.391 ORBIT STRUCTURE OF FINITE ZONE SECTOR OF TODA EQUATION AND EQUATION OF THE KdV (MKdV) TYPE |
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P. I. Holod1,2, O. V. Kisilevych3
1Bogolyubov Institute for Theoretical Physics
14-b Metrolohichna Str., Kyiv, UA-03143, Ukraine
2The University "Kiev-Mohyla Academy"
2 Skovoroda Str., Kyiv, UA-04070, Ukraine
3Lviv Commercial Academy
11 Samchuk Str., Lviv, UA-79011, Ukraine
Phase spaces of higher stationary equations hierarchy which belong to gauge equivalence Toda equation class are realized on co–joining action orbits of some sub–algebras in loop–algebra $sl(n,{\Bbb R})\otimes P(λ,λ^{-1})$. The equations themselves are represented in the form of integrable Eyler–Arnold equations. Established relations between dynamic variables of different gauge– equivalent equations generalize the known Miura transformation.