• Bargmann Symmetry Constraint and Binary Nonlinearization of Super NLS-MKdV Hierarchy
  • DOI: 10.4236/jmp.2013.45B002   PP.5 - 11
  • Author(s)
  • Sixing Tao, Hui Shi
  • ABSTRACT
  • An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.

  • KEYWORDS
  • Symmetry Constraints; Binary Nonlinearization; Super NLS-MKdV Hierarchy; Super Finite Dimensional Integrable Hamiltonian Systems
  • References
  • [1] Y. Cheng and Y. S. Li, “The Constraint of The Kadomt-sev-Petviashvili Equation and Its Special Solutions,” Physics Letters A , Vol. 157, No. 1, 1991, pp. 22-26. doi: 10.1016/0375-9601(91)90403-U

    [2] Y. Cheng, “Con-straints of the Kadomtsev-Petviashvili Hierarchy,” Journal of Mathematical Physics, Vol. 33, No. 11, 1992, pp. 3774-3782. doi: 10.1063/1.529875

    [3] W. X. Ma and W Strampp, “An Explicit Symmetry Constraint for the Lax Pairs of AKNS Sys-tems,” Physics Letters A, Vol. 185, No. 3, 1994, pp. 277-286. doi: 10.1016/0375-9601(94)90616-5

    [4] W. X. Ma, “New Finite-Dimensional Integrable Systems by Symmetry Constraint of the KdV Equations,” Journal of the Physical Society of Japan, Vol. 64, No. 4, 1995, pp. 1085-1091. doi: 10.1143/JPSJ.64.1085

    [5] Y. B. Zeng and Y. S. Li, “The Constraints of Potentials and the Finite-Dimensional Integrable Systems,” Journal of Mathematical Physics, Vol. 30, No. 8, 1989, pp.1679-1689. doi:10.1063/1.528253

    [6] C. W. Cao and X. G. Geng, “A Monconfocal Generator of Involutive Sys-tems and Three Associated Soliton Hierarchies,” Journal of Mathematical Physics, Vol. 2, No. 9, 1991, pp. 2323-2328. doi:10.1063/1.529156

    [7] W. X. Ma, “Symmetry Constraint of MKdV Equations by Binary Nonlinearization,” Physica A, Vol. 219, No. 3-4, 1995, pp. 467-481. doi:10.1016/0378-4371(95)00161-Y

    [8] W. X. Ma and R. G. Zhou, “Adjoint Symmetry Constraints Leading to Binaary Nonlinearization,” Journal of Nonlinear Mathematical Physics, Vol. 9, No. Suppl. 1, 2002, pp. 106-126.

    [9] W. X. Ma, “Bi-nary Bonlinearization for the Dirac Systems,” Chinese Annals of Mathematics, Series B, Vol. 18, No. 1, 1997, pp. 79-88.

    [10] J. S. He, J. Yu, Y. Cheng and R. G. Zhou, “Binary Bon linearization of the Super AKNS System,” Modern Physics Letters B, Vol. 22, No. 4, 2008, pp. 275-288. doi:10.1142/S0217984908014778

    [11] J. Yu, J. W. Han and J. S. He, “Binary Nonlinearization of the Super AKNS System under an Implicit Symmetry constraint,” Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 46, 2009, 465201. doi:10.1088/1751-8113/42/46/465201

    [12] J. Yu, J. S. He, W. X. Ma and Y. Cheng, “The Bargmann Symmetry Constraint and Binary Nonlinearization of the Super Dirac System,” Chinese Annals of Mathematics, Series B, Vol. 31, No. 3, 2010, pp. 361-372. doi:10.1007/s11401-009-0032-6

    [13] H. H. Dong and X. Z. Wang, “Lie Algebra and Lie Super Algebra for the Integrable Couplings of NLS-MKdV Hierarchy,” Communications in Nonlinear Science and Numeical Simulation, Vol. 14, No. 12, 2009, pp. 4071-4077. doi:10.1016/j.cnsns.2009.03.010

    [14] W. X. Ma, J. S. He and Z. Y. Qin, “A Supertrace Identity and Its Applications to Super Integrable Systems,” Journal of Mathe-matical Physics, Vol. 49, No. 3, 2008, 033511. doi:10.1063/1.2897036

    [15] X. B. Hu, “An Approach to Gen-erate Superextensions of Integrable Systems,” Journal of Physics A: Mathematical and General, Vol. 30, No. 2, 1997, pp. 619-632. doi:10.1088/0305-4470/30/2/023

    [16] W. X. Ma, B. Fuch-ssteiner and W. Oevel, “A 3×3 Matrix Spectral Problem for AKNS Hierarchy and Its Binary Nonlinearization,” Physica A, Vol. 233, No. 1-2, 1996, pp. 331-354. doi: 10.1016/S0378-4371(96)00225-7

    [17] W. X. Ma and Z. X. Zhou, “Binary Symmetry Constraints of N-wave Intersection Equations in 1+1 and 2+1 Dimensions,” Journal of Mathemat-ical Physics, Vol. 42, No. 9, 2001, pp. 4345-4382. doi:10.1063/1.1388898




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    December 11, 2013>>  February 16, 2014
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