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IMA Journal of Applied Mathematics 1979 23(2):121-130; doi:10.1093/imamat/23.2.121
© 1979 by Institute of Mathematics and its Applications
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The Equivalence of Bernoulli's Equation and a Set of Integral Relations for Periodic Waves

J. G. B. BYATT-SMITH

Department of Mathematics, University of Edinburgh

In a recent paper Longuet-Higgins (1978) discovered some new relations between Stokes' coefficients in the theory of periodic gravity waves. These were shown to give rise to a set of integral relations. In this paper we show that this set is complete in the sense that it is equivalent to Bernoulli's equation. We also show that a suitably redefined set exists in the theory of the solitary wave.


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