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

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

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.