Binary nonlinearization of the super AKNS system under an implicit symmetry constraint

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 46, 2009, Pages

  Yu, Jing ^a   Han, Jingwei ^a   He, Jingsong ^b,c  

^a HANGZHOU DIANZI UNIVERSITY   (China)

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

^c NINGBO UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 72449124832     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/46/465201     Document Type: Article

References (29)

1. Cao C W 1990 Nonlinearization of the Lax system for AKNS hierarchy Sci. China A 33 528-36
2. Konopelchenko B, Sidorenko J and Strampp W 1991 (1+1)-dimensional integrable systems as symmetry constraints of (2+1)-dimensional systems Phys. Lett. A 157 17-21
3. Cheng Y and Li Y S 1991 The constraint of the Kadomtsev-Petviashvili equation and its special solutions Phys. Lett. A 157 22-6
4. Cheng Y 1992 Constraints of the Kadomtsev-Petviashvili hierarchy J. Math. Phys. 33 3774-82
5. Ma W X and Strampp W 1994 An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems Phys. Lett. A 185 277-86
6. Zeng Y B 1995 The integrable system associated with higher-order constraint Acta Math. Sin. 38 642-52
7. Li Y S and Ma W X 2000 Binary nonlinearization of AKNS spectral problem under higher-order symmetry constraints Chaos Solitons Fractals 11 697-710
8. You Y, Yu J and Jiang Q Y 2008 An implicit symmetry constraint of the modified Korteweg-de Vries (mKdV) equation J. Zhejiang Univ. Sci. A 9 1457-62
9. Gurses M and Oguz O 1985 A super AKNS scheme Phys. Lett. A 108 437-40
10. Li Y S and Zhang L N 1988 Super AKNS scheme and its infinite conserved currents Nuovo Cimento A 93 175-83
11. Li Y S and Zhang L N 1988 A note on the super AKNS equations J. Phys. A: Math. Gen. 21 1549-52
12. Shaw J C and Tu M H 1998 Canonical gauge equivalences of the sAKNS and sTB hierarchies J. Phys. A: Math. Gen. 31 6517-23
13. Popowicz Z 1990 The fully supersymmetric AKNS equations J. Phys. A: Math. Gen. 23 1127-36
14. Aratyn H, Nissimov E and Pacheva S 1999 Supersymmetric Kadomtsev-Petviashvili hierarchy: 'ghost' symmetry structure, reductions, and Darboux-Bäcklund solutions J. Math. Phys. 40 2922-32
15. Ghosh S and Sarma D 2003 Soliton solutions of the N=2 supersymmetric KP equation J. Nonlinear Math. Phys. 10 526-38
16. Liu Q P and Mans M 1997 Darboux transformation for the Manin-Radul supersymmetric KdV equation Phys. Lett. B 394 337-42
17. Liu Q P and Mans Mz 2000 Darboux transformations for super-symmetric KP hierarchies Phys. Lett. B 485 293-300
18. Li Y S and Zhang L N 1990 Hamiltonian structure of the super evolution equation J. Math. Phys. 31 470-5
19. Oevel W and Popowicz Z 1991 The bi-Hamiltonian structure of fully supersymmetric Korteweg-de Vries systems Commun. Math. Phys. 139 441-60
20. Tu M H and Shaw J C 1999 Hamiltonian structures of generalized Manin-Radul super-kdV and constrained super KP hierarchies J. Math. Phys. 40 3021-34
21. He J S, Yu J, Cheng Y and Zhou R G 2008 Binary nonlinearization of the super AKNS system Mod. Phys. Lett. B 22 275-88
22. Cartier P, DeWitt-Morette C, Ihl M and Sämann C 2002 Supermanifolds-application to supersymmetry Multiple Facts of Quantization and Supersymmetry ed M Olshanetsky and A Vanishetin (River Edge, NJ: World Scientific) pp 412-57
23. Ma W X 1995 Symmetry constraint of MKdV equations by binary nonlinearization Physica A 219 467-81
24. Ma W X, Fuchssteiner B and Oevel W 1996 A 3×3 matrix spectral problem for AKNS hierarchy and its binary nonlinearization Physica A 233 331-54
25. Ma W X and Zhou Z X 2001 Binary symmetry constraints of N-wave interaction equations in 1+1 and 2+1 dimensions J. Math. Phys. 42 4345-82
26. Landi G, Marmo G and Vilasi G 1992 Remarks on the complete integrability of the dynamical systems with the fermionic variables J. Phys. A: Math. Gen. 25 4413-23
27. Zhou R G 2007 Integrable Rosochatisu deformations of the restricted soltion flows J. Math. Phys. 48 103510 17pp
28. Cao C W 1995 Classical integrable systems Soliton Theory and its Applications ed C H Gu (Berlin, Germany: Springer (Zhejiang Science and Technology Publishing House(Hangzhou, China)) pp 152-91
29. Zhou R G 1998 r-Matrix for the restricted KdV flows with the Neumann constraints J. Nonlinear Math. Phys. 5 181-9