Modulation solutions for the Benjamin-Ono equation (Q1809203)

Modulation solutions for three initial value problems for the Benjamin-Ono equation are studied. The first problem studied is the dispersive resolution of a step initial condition. An explicit solution of Gurevich-Pitaevskii type is derived, which explains the dispersive resolution of the step in terms of modulations. The second problem is the dispersive resolution of a breaking initial condition, while the third problem is the generation of a second phase as the result of the evolution of a modulated single phase wave. Again explicit modulation solutions for these problems are derived.