Pulsating multiplet solutions of quintic wave equations

Numerical studies are used to demonstrate that, in addition to supporting c onventional solitons, the quintic Korteweg-de Vries equation, u(t) + (u(2)) x = u(xxxxx), and its regularized version, u(t) + (u(2))(x) + u(txxxx) = 0, support multihumped solitary waves (doublets, triplets, quadruplets, etc.) , referred to collectively as multiplets. Their peaks pulsate as they trave l and undergo nearly elastic collisions with other multiplets. An N-humped multiplet can pulsate thousands of cycles before disassociating into an (N - 1)-humped multiplet and a single-peak solitary wave (singlet). Although m ultiplets are easily created from an initial wide compact pulse, they rarel y are formed by fusing singlets or multiplets in collisions. We describe th e emergence and evolution of multiplets, their nearly elastic collision dyn amics, and their eventual decomposition into singlets. To consider the effe ct of cubic dispersion on the solution of these equations, we also study mu (t) + (u(2)), + eta u(xxx) = delta u(xxxxx). The impact of cubic dispersion critically depends on the sign of eta and its amplitude. For sufficiently large eta > eta(1) > 0, only a train of singlets emerge from an initial pul se with compact support. If eta is decreased, multiplets begin to emerge le ading the train of singlets. The number of humps in the multiplet increases as tl is decreased, until below a critical point eta < eta(infinity) < 0 t he initial pulse decomposes into highly oscillatory waves. Copyright (C) 19 98 Elsevier Science B.V.