Chinese Quarterly Journal of Mathematics ›› 2009, Vol. 24 ›› Issue (3): 453-457.

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The Uniformly Valid Solution for a Top System of Two Free Dimensions with Parameter

  

  1. Department of Mathematics, Huzhou Teachers College

  • Received:2006-03-21 Online:2009-09-30 Published:2023-06-30
  • About author: OUYANG Cheng(1964- ), female, native of Taining, Fujian, M.S.D., a professor of Huzhou Teachers College, engages in singular perturbation theory.
  • Supported by:
     Supported by the NNSF of China(10471039); Supported by the Natural Science Foundation of Zhejiang Province(Y606268); Supported by the E-Institutes of Shanghai Municipal Education Commission(E03004);

Abstract: A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed. Using the multiple scale method, its uniformly valid asymptotic solution, which is expressed by complex amplitudes, of the first order is obtained. And solvable conditions satisfied by the complex amplitudes are given, and then the relative result is generalized.

Key words: uniformly valid, asymptotic solution, solvable condition, multiple scale method

CLC Number: