arXiv subjects

Ilya Bogaevskii

Publications and source records attributed to Ilya Bogaevskii.

2 recordsLinked to original sources

arXiv2026

Asymptotic solutions: glancing trajectories, Lagrangian singularities, and Bessel cylinders

We find a normal form for the simplest Lagrangian singularity appearing as the projection onto the space-energy of a solution to the Hamilton-Jacobi equation. Using this normal form we approximate asymptotic solutions of an equation $(\widehat{H}-E_0) \, u_h = f_h$ with a semiclassical distribution $f_h$ microlocalized on a Lagrangian manifold $Λ_0$ when $E_0$ is a critical value of the restriction $H|_{Λ_0}$.

math-ph↗

arXiv2023

Lagrangian intersections and glancing points: typical transitions of phase in semiclassical approximations

Given a semiclassical distribution $f_h$ microlocalized on a Lagrangian manifold $Λ_0$, $H\in C^\infty( T^\ast {\bf R}^n)$, and $H=E$ a regular energy surface, we find asymptotic solutions of the PDE $(H(x,\widehat{p})-E) \, u_h (x,E)=f_h(x)$ in terms of the Maslov canonical operator, when the Hamilton vector field $v_H$ fails to be transverse to $Λ_0$ at some points.

math-ph↗