Asymptotic expansions for some integrals of quotients with degenerated divisors

Abstract

We study asymptotic expansion as $\nu \to 0$ for integrals over ${\mathbb{R}}^{2d}=\{(x,y)\}$ of quotients $F(x,y)/((x\cdot y{)}^2+(\nu \Gamma (x,y){)}^2{)}^{-1}$, where $\Gamma$ is strictly positive and $F$ decays at infinity sufficiently fast. Integrals of this kind appear in description of the four--waves interactions.

Cited by in corpus (1)

• Asymptotic expansions for a class of singular integrals emerging in non-linear wave systems