Some new relations are given between the kinetic and potential energies of a solitary wave. In particular, the Lagrangian is expressed as an integral involving the total energy. Alternative proofs are also given of two other exact relations satisfied by the profile of the wave. These relations are used to derive some very simple but close approximations to the form of the wave of maximum amplitude.
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M. S. Longuet‐Higgins (1974) studied this question.
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