Weakly nonlocal gravity–capillary solitary waves

There is evidence from previous analytical work based on a model equation and from numerical computations that gravity–capillary solitary waves in a liquid layer are nonlocal—they feature oscillatory tails of constant amplitude—when the Bond number τ is less than 1/3. Here, the full gravity–capillary wave problem is examined and these tails are calculated asymptotically in the weakly nonlinear regime. For given values of τ (0