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Dressing transformations and Poisson group actions. (English) Zbl 0673.58019
See the review of Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 150, 119-142 (1986; Zbl 0602.35108).

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
35A30 Geometric theory, characteristics, transformations in context of PDEs
53D50 Geometric quantization
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q99 Partial differential equations of mathematical physics and other areas of application
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[1] Date E., Jimbo M., Kashiwara M. and Miwa T., Transformation groups for soliton equation. P roc. Japan. Acad. 57A (1981). 3806-3818, Physica 4D (1982), 343-365; Publ. RIMS Kyoto Univ., 18 (1982), 1077-1119. · Zbl 0571.35099
[2] Zakharov V. E. and Shabat A. B., Integration of nonlinear equations by the inverse scattering method II, Fund. Anal, and its applications 13 (1979), 166-174. · Zbl 0448.35090
[3] Segal G. and Wilson G., Loop groups and equations of KdV type, Publ. Math. I. H. E. S., 21 (1985), 1-64 · Zbl 0592.35112
[4] Wilson G., Habillage et fonctions T, C. R. Acad. Sci. Paris, 299 (1984), 587-590. · Zbl 0564.35086
[5] Dolan L., Kac-Moody algebras and exact solvability in hadronic physics, Phys. Rep. 109 (1984), 1-94.
[6] Davies M. C. et al. Hidden symmetries as canonical transformations for chiral model, Phys. Lett., 119B (1982), 187-192.
[7] Semenov-Tian-Shansky M. A., What is the classical r-matrix, Funct. Anal, and its Applications, 17 (1983), 259-272. · Zbl 0535.58031 · doi:10.1007/BF01076717
[8] Drinfel’d V. G., Hamiltonian structures on Lie groups, Lie bialgebras and the geomet- ric meaning of Yang-Baxter equations, DAN SSSR, 268, 285-287, in Russian.
[9] Weinstein A., Local structure of Poisson manifolds, J. Diff. Geom.,18 (1983), 523-558. · Zbl 0524.58011
[10] Faddeev L. D., Integrable models in 1 + 1 dimensional quantum field theory, Les H ouches Lectures 1982.
[11] Gel’fand I. M. and Dorfman I. Ya., Hamiltonian operators and the classical Yang- Baxter equation, Funkz. analiz i ego prilozh., 16 (1982), no. 4, 1-9, in Russian. · Zbl 0527.58018 · doi:10.1007/BF01077846
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