High-Frequency Two-Dimensional Asymptotic Standing Coastal-Trapped Waves in Nearly Integrable Case

Abstract

This paper is a continuation of research started in [7] devoted to explicit asymptotic formulas for standing coastal-trapped waves. Our main goal is to construct formal asymptotic eigenfunctions of the wave operator $\langle \nabla, D(x)\nabla\rangle$ (the spatial part of the wave operator) corresponding to the eigenvalue $\omega\to\infty$ in a nearly integrable case.