Asymptotic expansions for a class of singular integrals emerging in nonlinear wave systems

  title={Asymptotic expansions for a class of singular integrals emerging in nonlinear wave systems},
  author={Andrey Dymov},
  journal={Theoretical and Mathematical Physics},
  • A. Dymov
  • Published 19 September 2022
  • Materials Science
  • Theoretical and Mathematical Physics
Abstract We find asymptotic expansions as $$\nu\to 0$$ for integrals of the form $$\int_{\mathbb{R}^d}F(x)/(\omega^2(x)+\nu^2)\,dx$$ , where sufficiently smooth functions $$F$$ and $$\omega$$ satisfy natural assumptions on their behavior at infinity and all critical points of $$\omega$$ in the set $$\{\omega(x)=0\}$$ are nondegenerate. These asymptotic expansions play a crucial role in analyzing stochastic models for nonlinear waves systems. We generalize a result of Kuksin that a similar… 
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