Applied Mathematics and Mechanics (English Edition) ›› 1982, Vol. 3 ›› Issue (4): 599-606.

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ON MATHIEU EQUATION’S FIRST-ORDER INSTABLE ZONE AND ITS APPLICATION IN CYCLOTRON

Luo Shi-yu   

  1. Institute of Modern Physics, Academia Sinica, Lanzhou
  • Received:1980-08-01 Online:1982-07-18 Published:1982-07-18

Abstract: The v2=1/2 resonance was analyzed approximately, by using stability of Mathieu equation’s solutions and the method of transfer matrix, and gradient amplitude of a critical perturbed field was derived.

Key words: nonlinear resonance, weakly nonlinear Stokes waves, a free surface current, rippled beds, dynamical system

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