Note on a parametrically excited, trapped cross-wave

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Abstract
The cubic Schrödinger equation, which governs the complex amplitude of a cross-wave that is subharmonically excited by a symmetric wavemaker in a deep wave tank (Jones 1984), is solved for prescribed boundary conditions at the wavemaker and a null condition at infinity. This solution (which is a limiting case of a one-parameter family of cnoidal waves) typically describes a trapped wave that decays exponentially in a semi-infinite tank, although it may be fitted to a tank of finite length for a particular combination of parameters. It is closely related to the solution for trapped waves excited through vertical oscillation of a long channel (Wu, Keolian & Rudnick 1984).

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