Secular series and renormalization group for amplitude equations.
We have developed a technique that circumvents the process of elimination of secular terms [L.-Y. Chen, N. Goldenfeld, and Y. Oono, Phys. Rev. E 54, 376 (1996)] and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems.
Kirkinis
Eleftherios
E
Applied Mathematics, University of Washington, Seattle, Washington 98195-2420, USA. kirkinis@amath.washington.edu