A differential equation in the theory of resonant oscillations of water waves

C. J. Amick; J. F. Toland

doi:10.1017/S0308210500024227

A differential equation in the theory of resonant oscillations of water waves

C. J. Amick, J. F. Toland

Department of Mathematical Sciences

University of Chicago

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the problem [formula omitted] has a unique solution and that the asymptotic behaviour of this solution as x→− ∞ is given by [formula omitted], for some constant φ. Here B ≠ 0 depends on ε and [formula omitted]. In particular there are no even solutions of problem (*) for any ε > 0.

Original language	English
Pages (from-to)	15-26
Number of pages	12
Journal	Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume	114
Issue number	1-2
DOIs	https://doi.org/10.1017/S0308210500024227
Publication status	Published - 1 Jan 1990

ASJC Scopus subject areas

General Mathematics

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title = "A differential equation in the theory of resonant oscillations of water waves",

abstract = "We show that the problem [formula omitted] has a unique solution and that the asymptotic behaviour of this solution as x→− ∞ is given by [formula omitted], for some constant φ. Here B ≠ 0 depends on ε and [formula omitted]. In particular there are no even solutions of problem (*) for any ε > 0.",

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AB - We show that the problem [formula omitted] has a unique solution and that the asymptotic behaviour of this solution as x→− ∞ is given by [formula omitted], for some constant φ. Here B ≠ 0 depends on ε and [formula omitted]. In particular there are no even solutions of problem (*) for any ε > 0.

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A differential equation in the theory of resonant oscillations of water waves

Abstract

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