Health & Environmental Research Online (HERO)


Print Feedback Export to File
6300686 
Journal Article 
A perturbation procedure for weakly coupled oscillators 
Kabakow, H 
1972 
Yes 
International Journal of Non-Linear Mechanics
ISSN: 0020-7462 
Elsevier 
7 
1 
125-137 
English 
Problems involving systems of oscillators with weak non-linear (polynomial) coupling are of interest in connection with the ergodic problem of statistical mechanics and as simple models of non-linear interactions. These systems have been studied by Ford and Waters [1] and Jackson [2, 3], who used variations of the Wigner-Brillouin (WB) procedure to calculate the dynamics. The principal difficulty with WB is that it places too strong a restriction on the analytic form the answer can take. With this restriction, the famous “small divisor” problem can emerge at some point in the calculation. This paper describes the "N-timing" procedure (of which WB is essentially a special case), shows how it can be applied to calculate the long-time dynamics of coupled oscillator systems, and establishes by computer experiments the accuracy of N-timing for a particular example. A subsequent paper will present an example in which small divisors arise and show how they can be eliminated by N-timing.