Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (1): 26-34.

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A FAMILY OF INTEGRABLE SYSTEMS OF LIOUVILLE AND LAX REPRESENTATION, DARBOUX TRANSFORMATIONS FOR ITS CONSTRAINED FLOWS

ZHANG Yu-feng1,2, ZHANG Hong-qing2   

  1. 1. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China;
    2. Basic Courses Department, Shandong University of Science and Technology, Tai’an, Shangdong 271019, P. R. China
  • Received:2000-10-16 Revised:2001-09-28 Online:2002-01-18 Published:2002-01-18
  • Supported by:

    the Chinese Basic Research "Mathematical Mechanization and a Platform for Automated Reasoning"(G1998030600)

Abstract: A family of integrable systems of Liouville are obtained by Tu pattern. Using higher-order potential-eigenfunction constraints, the integrable systems are factorized to two x- and tn-integrable Hamiltonian systems whose Lax representation and three kinds of Darboux transformations are presented.

2010 MSC Number: 

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