Abstract
We consider the generalized AKNS systems, introduced and discussed recently in [1]. We have shown that the dressing techniques both in matrix pseudo-differential operators and formal series with respect to the spectral parameter can be developed for these hierarchies.
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M. F. de Groot, T. J. Hollowood, and J. L. Miramontes,Commun. Math. Phys.,145, 57–84 (1992); N. J. Burrough, M. F. de Groot, T. J. Hollowood, and J. L. Miramontes,Commun. Math. Phys.,153, 187–215 (1993).
V. G. Kac and D. H. Peterson, “112 Construction of the Loop Group ofE 8,” in:Proceedings of Symposium on Anomalies, Geometry, and Topology, World Scientific, Singapore (1985), pp. 276–298.
V. G. Drinfeld and V. V. Sokolov,J. Sov. Math.,30, 1975–2036 (1984).
A. Digasperis, D. Lebedev, M. Olshanetsky, S. Pakuliak, A. Perelomov, and P. Santini,Commun. Math. Phys.,141, 133–151 (1991);J. Math. Phys.,33, No. 11, 3783–3793 (1992).
F. Delduc and L. Fehér,Conjugacy classes in the Weyl group admitting a regular eigenvector and integrable hierarchies, Preprint ENSLAPP-L-493/94.
F. ten Kroode and J. van de Leur,Commun. Math. Phys.,137, 67–107 (1991).
L. Fehér, J. Harnad, and I. Marshal,Commun. Math. Phys.,154, 181–214 (1993).
M. A. Semenov-Tian-Shansky, “Dressing transformation and Poisson Lie group action,”Publ. RIMS Kyoto Univ.,21, 1237 (1985).
D. Lebedev and S. Pakuliak,Comments on the Drinfeld-Sokolov Hamiltonian reduction. 1.gl(n) Case, Genova Univ. Preprint GEF-Th-9/1990.
I. M. Gelfand and L. A. Dickey, Preprint Inst. Appl. Math. (1978).
I. M. Gelfand and L. A. Dickey,Funct. Anal. Appl.,11, 93–104 (1977).
Yu. I. Manin,J. Sov. Math.,11, 1–122 (1979).
G. Wilson,Math. Proc. Cambridge. Philos. Soc.,86, 131–143 (1979);Q. J. Math. Oxford,32, 491–512 (1981).
D. Lebedev and S. Pakuliak,Phys. Lett. A,160, 173–178 (1991).
A. Newell,Solitons in Mathematics and Physics, CBMS 48 SIAM, Philadelphia (1985).
V. G. Kac and J. W. van de Leur, “Then-component KP hierarchy and representation theory,” in:Important Developments in Soliton Theory, Springer Series in Nonlinear Dynamics (A. S. Fokas and V. E. Zakharov, eds.) (1993), pp. 302–343.
L. A. Dickey,Soliton Equations and Hamiltonian Systems, World Scientific, Singapore (1991).
L. A. Dickey,J. Math. Phys.,32, No. 11, 2996–3002 (1991).
M. J. Bergvelt and A. P. E. ten Kroode,J. Math. Phys.,29, No. 6, 1308–1320 (1988).
C. R. Fernández-Pousa, M. V. Gallas, J. L. Miramontes, and J. S. Guillén,W-Algebras from soliton equations and Heisenberg subalgebras, Preprint Univ. of Santiago, US-FT/13-94, hep-th/9409016.
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On leave of absence from the ITP, Kiev 252143, Ukraine. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 3, pp. 422–436, June, 1995.
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Holod, P., Pakuliak, S. The dressing techniques for intermediate hierarchies. Theor Math Phys 103, 668–680 (1995). https://doi.org/10.1007/BF02065866
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DOI: https://doi.org/10.1007/BF02065866