TY  - JOUR
A1  - Rosenau, Philip
A1  - Pikovskij, Arkadij
T1  - Solitary phase waves in a chain of autonomous oscillators
T2  - Chaos : an interdisciplinary journal of nonlinear science
N2  - In the present paper, we study phase waves of self-sustained oscillators with a nearest-neighbor dispersive coupling on an infinite lattice. To analyze the underlying dynamics, we approximate the lattice with a quasi-continuum (QC). The resulting partial differential model is then further reduced to the Gardner equation, which predicts many properties of the underlying solitary structures. Using an iterative procedure on the original lattice equations, we determine the shapes of solitary waves, kinks, and the flat-like solitons that we refer to as flatons. Direct numerical experiments reveal that the interaction of solitons and flatons on the lattice is notably clean. All in all, we find that both the QC and the Gardner equation predict remarkably well the discrete patterns and their dynamics.
Y1  - 2020
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/59072
SN  - 1054-1500
SN  - 1089-7682
VL  - 30
IS  - 5
PB  - American Institute of Physics, AIP
CY  - Melville, NY
ER  -