Radiating solitary waves of a model evolution equation in fluids of finite depth

Abstract

The evolution equation proposed by Kubota et al. [J. Hydronautics 12 (1978) 157–165] and Joseph [J. Phys. A 10 (1977) 225–227] for long waves in stratified fluids of finite depth is considered. Under a small third-order-derivative dispersive perturbation, solitary-wave solutions to this model equation become weakly nonlocal — they develop oscillatory tails of infinite extent and exponentially small amplitude. Here, these tails are calculated asymptotically following a perturbation procedure in the wavenumber domain.