Abstract—An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for a super integrable hierarchy. Under the obtained symmetry constraint, the n-th flow of the super integrable 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.

Index Terms—Symmetry constraints, binary nonlinearization, super integrable hierarchy, super finite-dimensional integrable Hamiltonian systems.

Sixing Tao is with School of Mathematics and Information Science, Shangqiu Normal University, Shangqiu 476000, PR China (email:taosixing@163.com).

Cite: Sixing Tao, "Bargmann Symmetry Constraint and Binary Nonlinearization of a Super Integrable Hierarchy," International Journal of Applied Physics and Mathematics vol. 5, no. 1, pp. 29-38, 2015.