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.

Renormalization group interpretation of the Born and Rytov approximations.

In this paper the method of renormalization group (RG) [Phys. Rev. E54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media.

Reduction of amplitude equations by the renormalization group approach.

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach [L.-Y.