Wave breaking in the short-pulse equation (2009)
Liu, Yue, Pelinovsky, Dmitry, Sakovich, Anton
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 of...
Wave breaking in the Ostrovsky--Hunter equation (2009)
Liu, Yue, Pelinovsky, Dmitry, Sakovich, Anton
The Ostrovsky--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 the...
Global well-posedness of the short-pulse and sine-Gordon equations in energy space (2008)
Pelinovsky, Dmitry, Sakovich, Anton
We prove global well-posedness of the short-pulse equation with small initial data in Sobolev space H^s for an integer s>=2. Our analysis relies on local well-posedness results of Schafer and Wayne,...
A new integrable generalization of the Korteweg - de Vries equation (2007)
Karasu-Kalkanli, Ayse, Karasu, Atalay, Sakovich, Anton, Sakovich, Sergei, Turhan, Refik
A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg - de Vries equation with a source. A Lax representation and a...
On Transformations of the Rabelo Equations (2007)
Sakovich, Anton, Sakovich, Sergei
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 some...
On Transformations of the Rabelo Equations (2007)
Anton Sakovich, Sergei Sakovich
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 some...
Solitary wave solutions of the short pulse equation (2006)
Sakovich, Anton, Sakovich, Sergei
An exact nonsingular solitary wave solution of the Schafer-Wayne short pulse equation is derived from the breather solution of the sine-Gordon equation by means of a transformation between these two...
The short pulse equation is integrable (2004)
Sakovich, Anton, Sakovich, Sergei
We prove that the Schafer-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 SPE...