Chinese Quarterly Journal of Mathematics ›› 2005, Vol. 20 ›› Issue (3): 232-237.

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The Rigid Body Type Poisson Structure for the Constrained NLS System

  

  1. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China;Department of Mathematics, Shangqiu Normal University, Shangqiu 476000, China
  • Received:2005-06-27 Online:2005-09-30 Published:2024-01-11
  • About author:Du Dian-lou(1964-),male,native of Luoyang,Henan,an associate professor of Zhengzhou University,Ph,D.,engages in solution and integrable systems.
  • Supported by:
     Foundation item: Supported by the National Natural Science Foundation of China(10471132) Supported by the Youth Teacher Foundation and Natural Science Foundation of Henan Education Department(2004110006);

Abstract: A constrained system associated with a 3×3 matrix spectral problem of the nonlinear Schrodinger(NLS) hierarchy is proposed. It is shown that the constrained system is a Hamiltonian system with the rigid body type Poisson structure on the Poisson manifold R3N. Further, the reduction of the constrained system extended to the common level set of the complex cones is proved to be the constrained AKNS system on C2N.

Key words:  constrained , system;Poisson , structure;reduction

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