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A.S. Fokas, R.H.J. Grimshaw, and D.E. Pelinovsky

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On the asymptotic integrability of a higher-order
evolution equation describing internal waves in a deep fluid

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J. Math. Phys. 37, 3415-3421 (1996)

**Abstract:**

A higher-order nonlocal evolution equation describing
internal waves in a deep fluid is shown to be asymptotically
integrable only if the coefficients of the higher-order
terms satisfy certain constraints. In this case, the nonlocal
equation can be transformed to the integrable Benjamin-Ono
equation. The asymptotic integrability of the
reductions of the higher-order evolution equation to a
complex Burgers equation, to an envelope-wave equation,
and to a finite-dimensional dynamical system is also
considered.