Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation

Abstract:
Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. It is shown how the nature of the waves may be categorized in a simple way by considering the value of a certain single combination of parameters. The periodic waves may be smooth humps, cuspons, loops or parabolic corner waves. The latter are shown to be the maximum-amplitude limit of a one-parameter family of periodic smooth-hump waves. The solitary waves may be smooth humps, cuspons or loops.