332 citations · 917 across the 8 of their papers we have counts for
8 papers
Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations
Dmitry Pelinovsky, Anton Sakovich
We prove the most general theorem about spectral stability of multi-site breathers in the discrete Klein-Gordon equation with a small coupling constant. In the anti-continuum limit…
Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation
Dmitry Pelinovsky, Anton Sakovich
Discrete solitons of the discrete nonlinear Schrödinger (dNLS) equation become compactly supported in the anti-continuum limit of the zero coupling between lattice sites. Eigenvalu…
Wave breaking in the short-pulse equation
Yue Liu, Dmitry Pelinovsky, Anton Sakovich
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 meth…
Wave breaking in the Ostrovsky--Hunter equation
Yue Liu, Dmitry Pelinovsky, Anton Sakovich
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 brea…
Global well-posedness of the short-pulse and sine-Gordon equations in energy space
Dmitry Pelinovsky, Anton Sakovich
We prove global well-posedness of the short-pulse equation with small initial data in Sobolev space . Our analysis relies on local well-posedness results of Schäfer & Wayne, t…
A new integrable generalization of the Korteweg - de Vries equation
Ayse Karasu-Kalkanli, Atalay Karasu, Anton Sakovich +2
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 r…