The Ostrovskyâ€“Hunter equation governs evolution of shallow water waves on a rotating fluid in the limit of small high-frequency dispersion. Sufficient conditions for the wave breaking in theâ€¦ (More)

Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method ofâ€¦ (More)

We prove global well-posedness of the short-pulse equation with small initial data in Sobolev space Hs for an integer s â‰¥ 2. Our analysis relies on local well-posedness results of SchÃ¤fer & Wayneâ€¦ (More)

We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to someâ€¦ (More)

We prove that the SchÃ¤ferâ€“Wayne short pulse equation (SPE) which describes the propagation of ultra-short optical pulses in nonlinear media is integrable. First, we discover a Lax pair of the SPEâ€¦ (More)

We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to someâ€¦ (More)