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<p>Exact solutions for the shallow water equation in an infinite rectilinear channel with a small obstruction of the water bed are constructed in the form of infinite convergent series in powers of the small parameter characterizing the height of the obstruction. These solutions describe embedded trapped modes which are localized at the obstruction and decay at infinity. A simple formula for their frequencies is obtained.</p>

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Embedded trapped modes for the shallow water equation in an infinite channel

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  • 发表日期：

    2025年2月25日

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  • M. I. Romero Rodríguez

摘要

Exact solutions for the shallow water equation in an infinite rectilinear channel with a small obstruction of the water bed are constructed in the form of infinite convergent series in powers of the small parameter characterizing the height of the obstruction. These solutions describe embedded trapped modes which are localized at the obstruction and decay at infinity. A simple formula for their frequencies is obtained.