Hamiltonian structure of the super evolution equation. (English) Zbl 0705.58024

Li, Yishen; Zhang, Lining

J. Math. Phys. 31, No. 2, 470-475 (1990).

Using the so-called constrained variational calculus introduced by Y. Zheng, the first author and D. Chen [Sci. Sin., Ser. A 24, 138 (1986)] the authors cast the supersymmetric generalization [due to M. Gürses and O. Oguz, Phys. Lett. A 108, 437 (1985)] of the soliton equations of M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur [Stud. Appl. Math. 53, 249-315 (1974; Zbl 0408.35068)] into Hamiltonian form.
It must be stated that because of misprints, sloppy notation and confusing organization the reading of the article is a nuisance.

Reviewer: H.Rumpf

MSC:

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.)
35Q51	Soliton equations

Keywords:

super AKNS system; supersymmetric symplectic matrix; Hamiltonian solitons

Citations:

Zbl 0408.35068

References:

[1]	DOI: 10.1016/0375-9601(84)90693-5
[2]	DOI: 10.1016/0375-9601(85)90033-7
[3]	DOI: 10.1143/PTP.72.641 · Zbl 1074.81578
[4]	DOI: 10.1063/1.527309 · Zbl 0614.70014
[5]	Zheng Yun-bo, Sci. Sinica A 24 pp 138– (1986)
[6]	Tu Gui-zhang, Science Building 29 pp 1227– (1984)
[7]	DOI: 10.1007/BF02819989