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

TL;DR

This paper develops asymptotic formulas for high-frequency standing coastal-trapped waves in nearly integrable systems, advancing understanding of wave eigenfunctions at large eigenvalues.

Contribution

It constructs formal asymptotic eigenfunctions for the wave operator in the nearly integrable case, extending previous work on coastal-trapped waves.

Findings

Explicit asymptotic formulas for eigenfunctions at high frequencies

Extension of previous models to nearly integrable systems

Enhanced understanding of wave behavior in coastal regions

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.