253 citations · 3.1k across the 151 of their papers we have counts for
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Rogue periodic waves of the focusing NLS equation
Jinbing Chen, Dmitry E. Pelinovsky
Rogue waves on the periodic background are considered for the nonlinear Schrodinger (NLS) equation in the focusing case. The two periodic wave solutions are expressed by the Jacobi…
Krein Signature in Hamiltonian and -symmetric Systems
A. Chernyavsky, P. G. Kevrekidis, D. E. Pelinovsky
We explain the concept of Krein signature in Hamiltonian and -symmetric systems on the case study of the one-dimensional Gross-Pitaevskii equation with a real harmoni…
Spectral stability of shifted states on star graphs
Adilbek Kairzhan, Dmitry E. Pelinovsky
We consider the nonlinear Schrödinger (NLS) equation with the subcritical power nonlinearity on a star graph consisting of edges and a single vertex under generalized Kirchhoff…
Ground state of the conformal flow on
Piotr Bizoń, Dominika Hunik-Kostyra, Dmitry Pelinovsky
We consider the conformal flow model derived by Bizoń, Craps, Evnin, Hunik, Luyten, and Maliborski [Commun. Math. Phys. 353 (2017) 1179-1199] as a normal form for the conformally i…
Krein signature for instability of -symmetric states
Alexander Chernyavsky, Dmitry E. Pelinovsky
Krein quantity is introduced for isolated neutrally stable eigenvalues associated with the stationary states in the -symmetric nonlinear Schrödinger equation. Krein q…
Normal form for transverse instability of the line soliton with a nearly critical speed of propagation
Dmitry E. Pelinovsky
There exists a critical speed of propagation of the line solitons in the Zakharov-Kuznetsov (ZK) equation such that small transversely periodic perturbations are unstable for line…