The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems

Chinese Annals of Mathematics. Series B

Volumn 31, Issue 3, 2010, Pages 361-372

  Yu, Jing ^a,b   He, Jingsong ^b,d   Ma, Wenxiu ^c   Cheng, Yi ^b  

^a HANGZHOU DIANZI UNIVERSITY   (China)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^c NINGBO UNIVERSITY   (China)

^d UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

Binary nonlinearization; Super Dirac systems; Super finite dimensional integrable Hamiltonian systems; Symmetry constraints

Indexed keywords

EID: 77953083129     PISSN: 02529599     EISSN: 18606261     Source Type: Journal    
DOI: 10.1007/s11401-009-0032-6     Document Type: Article

References (26)

1. Konopelchenko, B., Sidorenko, J. and Strampp, W., (1 + 1)-dimensional integrable systems as symmetry constraints of (2 + 1)-dimensional systems, Phys. Lett. A, 157(1), 1991, 17-21.
2. Cheng, Y. and Li, Y. S., The constraint of the Kadomtsev-Petviashvili equation and its special solutions, Phys. Lett. A, 157(1), 1991, 22-26.
3. Cheng, Y., Constraints of the Kadomtsev-Petviashvili hierarchy, J. Math. Phys., 33(11), 1992, 3774-3782.
4. Ma, W. X. and Strampp, W., An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems, Phys. Lett. A, 185(3), 1994, 277-286.
5. Ma, W. X., New finite-dimensional integrable systems by symmetry constraint of the KdV equations, J. Phys. Soc. Japan, 64(4), 1995, 1085-1091.
6. Ma, W. X. and Zeng, Y. B., Binary constrained flows and separation of variables for soliton equations, ANZIAM J., 44(1) 2002, 129-139.
7. Zeng, Y. B. and Li, Y. S., The constraints of potentials and the finite-dimensional integrable systems, J. Math. Phys., 30(8), 1989, 1679-1689.
8. Cao, C. W., Nonlinearization of the Lax system for AKNS hierarchy, Sci. China Ser. A, 33(5), 1990, 528-536.
9. Cao, C. W. and Geng, X. G., A nonconfocal generator of involutive systems and three associated soliton hierarchies, J. Math. Phys., 32(9), 1991, 2323-2328.
10. Ma, W. X., Symmetry constraint of MKdV equations by binary nonlinearization, Phys. A, 219(3-4), 1995, 467-481.
11. Ma, W. X. and Zhou, R. G., Adjoint symmetry constraints leading to binary nonlinearization, J. Nonlinear Math. Phys., 9(Suppl. 1), 2002, 106-126.
12. Ma, W. X., Binary nonlinearization for the Dirac systems, Chin. Ann. Math., 18B(1), 1997, 79-88.
13. Popowicz, Z., The fully supersymmetric AKNS equations, J. Phys. A, 23(7), 1990, 1127-1136.
14. Gurses, M. and Oǧuz, O., A super AKNS scheme, Phys. Lett. A, 108(9), 1985, 437-440.
15. Liu, Q. P. and Manas, M., Darboux transformations for super-symmetric KP hierarchies, Phys. Lett. B, 485(1-3), 2000, 293-300.
16. Kupershmidt, B. A., A super Korteweg-de Vries equation: an integrable system, Phys. Lett. A, 102(5-6), 1984, 213-215.
17. Li, Y. S. and Zhang, L. N., Super AKNS scheme and its infinite conserved currents, Nuovo Cimento A, 93(2), 1986, 175-183.
18. Li, Y. S. and Zhang, L. N., Hamiltonian structure of the super evolution equation, J. Math. Phys., 31(2), 1990, 470-475.
19. He, J. S., Yu, J., Cheng, Y., et al, Binary nonlinearization of the super AKNS system, Modern Phys. Lett. B, 22(4), 2008, 275-288.
20. Ma, W. X., He, J. S. and Qin, Z. Y., A supertrace identity and its applications to super integrable systems, J. Math. Phys., 49(3), 2008, 033511.
21. Hu, X. B., An approach to generate superextensions of integrable systems, J. Phys. A, 30(2), 1997, 619-632.
22. Ma, W. X., Fuchssteiner, B. and Oevel, W., A 3 × 3 matrix spectral problem for AKNS hierarchy and its binary nonlinearization, Phys. A, 233(1-2), 1996, 331-354.
23. Ma, W. X. and Zhou, Z. X., Binary symmetry constraints of N-wave interaction equations in 1 + 1 and 2 + 1 dimensions, J. Math. Phys., 42(9), 2001, 4345-4382.
24. Jetzer, F., Completely integrable system on supermanifolds, Thesis of the degree of Doctor of Philosophy, Department of Mathematics and Statistics, McGill University, Montréal, 1999.
25. Shander, V. N., Complete integrability of ordinary differential equations on supermanifolds, Funct. Anal. Appl., 17(1), 1983, 74-75.
26. Cartier, P., DeWitt-Morette, C., Ihl, M., et al, Supermanifolds-application to supersymmetry, Maultiple Facets of Quantization and Supersymmetry, M. Olshanetsky and A. Vanishetin (eds.), World Scientific Publishing, River Edge, 2002, 412-457. arXiv: math-ph/0202026v1.