Solitary wave families of NLPDES via reversible systems theory
The Ostrovsky equation is an important canonical model for the undirectional propagation of weakly nonlinear long surface and internal waves in a rotating, mviscid and incompressible fluid. Since solitary wave solutions often play a central role in the long-time evolution of an inital disturbance. we consider such solutions here (via the normal form approach) within the framework of reversible system theory. Resides confirming the existence of the known family of solitary waves and its reduction to the Kdv limit. w we find a second family of multihumped (or N-pulse) solutions, as well as a contimum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solutions. The second and third families of solutions occur in regions of parameter space distinct from the known solitary wave solutions and are thus entirely new directions for future work, including on other NLPDEs, are also mentioned. (C) 2009 IMACS Published by Elsevier B.V. All rights reserved.
solitary wave families reversible systems theory