In the scope of my PhD studies we work on existence and stability of localized solutions to lattice differential equations such as the discrete nonlinear Schrodinger equation and discrete Klein–Gordon equations.
A copy of my MSc thesis "Well-posedness of nonlinear wave equations in
characteristic coordinates" is available
here.
| Dmitry Pelinovsky, Anton Sakovich. Multi-site breathers in Klein–Gordon lattices: stability, resonances, and bifurcations. (submitted to Nonlinearity)
|
ArXiv
|
Journal
|
| Dmitry Pelinovsky, Anton Sakovich. Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation. Physica D 240 (2011) 265–281
|
ArXiv
|
Journal
|
Yue Liu, Dmitry Pelinovsky, Anton Sakovich. Wave breaking in the Ostrovsky–Hunter equation. SIAM J. Math. Anal. 42 (2010) 1967–1985
|
ArXiv
|
Journal
|
| Dmitry Pelinovsky, Anton Sakovich. Global well-posedness of the short-pulse and sine-Gordon equations in energy space. Commun. Part. Diff. Eq. 35 (2010) 613–629
|
ArXiv
|
Journal
|
| Yue Liu, Dmitry Pelinovsky, Anton Sakovich. Wave breaking in the short-pulse equation. Dynam. Part. Differ. Eq. 6 (2009) 291–310
|
ArXiv
|
Journal
|
| Ayse Karasu-Kalkanli, Atalay Karasu, Anton Sakovich, Sergei Sakovich, Refik Turhan. A new integrable generalization of the Korteweg – de Vries equation. J. Math. Phys. 49 (2008) 073516 (10 pp.)
|
ArXiv
|
Journal
|
| Anton Sakovich, Sergei Sakovich. On transformations of the Rabelo equations. SIGMA 3 (2007) 086 (8 pp.)
|
ArXiv
|
Journal
|
| Anton Sakovich, Sergei Sakovich. Solitary wave solutions of the short pulse equation. J. Phys. A: Math. Gen. 39 (2006) L361–L367
|
ArXiv
|
Journal
|
| Anton Sakovich, Sergei Sakovich. The short pulse equation is integrable. J. Phys. Soc. Jpn. 74 (2005) 239–241
|
ArXiv
|
Journal
|