CYLINDRICAL ENVELOPE SOLITARY WAVES

The method of multiple-scales is used to investigate the nonlinear modulation of capillary-gravity waves with cylindrical symmetry. We find that the evolution of wave-packets is described by a nonlinear schrödinger-like equation i(U + U/2r) + αU_ξξ + β|U|²U = 0. Some exact and explicit cylindrical envelope solitary wave solutions are also obtained by means of variable transformations.