Higher-order modulation effects on solitary wave envelopes in deep water Part 2. Multi-soliton envelopes

Abstract

Previous experimental and numerical work indicates that an initially symmetric deep-water wave pulse of uniform frequency and moderately small steepness evolves in an asymmetric manner and eventually separates into distinct wave groups, owing to higher-order modulation effects, not accounted for by the nonlinear Schrödinger equation (NLS). Here perturbation methods are used to provide analytical confirmation of this group splitting on the basis of the more accurate envelope equation of Dysthe (1979). It is demonstrated that an initially symmetric multisoliton wave envelope, consisting of N bound NLS solitons, ultimately breaks up into N separate groups; a procedure is devised for determining the relative speed changes of the individual groups. The case of a bi-soliton (N = 2) is discussed in detail, and the analytical predictions are compared to numerical results.