253 citations · 3.1k across the 151 of their papers we have counts for
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Existence and stability of PT-symmetric vortices in nonlinear two-dimensional square lattices
Haitao Xu, Panayotis G. Kevrekidis, Dmitry E. Pelinovsky
Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schrödinge…
Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations
D. Pelinovsky, T. Penati, S. Paleari
Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approx…
Ground state on the dumbbell graph
Jeremy L. Marzuola, Dmitry E. Pelinovsky
We consider standing waves in the focusing nonlinear Schrödinger (NLS) equation on a dumbbell graph (two rings attached to a central line segment subject to the Kirchhoff boundary…
Dimer with gain and loss: Integrability and -symmetry restoration
I. V. Barashenkov, D. E. Pelinovsky, P. Dubard
A -symmetric nonlinear Schrödinger dimer is a two-site discrete nonlinear Schrödinger equation with one site losing and the other one gaining energy at the same rate.…
Self-similar solutions for reversing interfaces in the nonlinear diffusion equation with constant absorption
Jamie M. Foster, Dmitry E. Pelinovsky
We consider the slow nonlinear diffusion equation subject to a constant absorption rate and construct local self-similar solutions for reversing (and anti-reversing) interfaces, wh…
Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices
Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Dmitry E. Pelinovsky
In the present work, we explore the possibility of excited breather states in a nonlinear Klein--Gordon lattice to become nonlinearly unstable, even if they are found to be spectra…