50 citations · 59 across the 23 of their papers we have counts for
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On the Existence of Generalized Breathers and Transition Fronts in Time-Periodic Nonlinear Lattices
Christopher Chong, Dmitry E. Pelinovsky, Guido Schneider
We prove the existence of a class of time-localized and space-periodic breathers (called q-gap breathers) in nonlinear lattices with time-periodic coefficients. These q-gap breathe…
Turing bifurcation in the Swift-Hohenberg equation on deterministic and random graphs
Georgi S. Medvedev, Dmitry E. Pelinovsky
The Swift-Hohenberg equation (SHE) is a partial differential equation that explains how patterns emerge from a spatially homogeneous state. It has been widely used in the theory of…
Validity of the weakly-nonlinear solution of the Cauchy problem for the Boussinesq-Ostrovsky equation
K. R. Khusnutdinova, K. R. Moore, D. E. Pelinovsky
We consider the initial-value problem for the regularized Boussinesq-Ostrovsky equation in the class of periodic functions. Validity of the weakly-nonlinear solution, given in term…
Bifurcation of gap solitons in periodic potentials with a sign-varying nonlinearity coefficient
Juan Belmonte-Beitia, Dmitry Pelinovsky
We address the Gross--Pitaevskii (GP) equation with a periodic linear potential and a periodic sign-varying nonlinearity coefficient. Contrary to the claims in the previous works o…
Travelling kinks in discrete phi^4 models
O. F. Oxtoby, D. E. Pelinovsky, I. V. Barashenkov
In recent years, three exceptional discretizations of the phi^4 theory have been discovered [J.M. Speight and R.S. Ward, Nonlinearity 7, 475 (1994); C.M. Bender and A. Tovbis, J. M…