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Nonlinear internal models for output regulation
In this paper we show how nonlinear internal models can be effectively used
in the design of output regulators for nonlinear systems. This result provides
a significant enhancement of the non-equilibrium theory for output regulation,
which we have presented in the recent paper entitled "Limit Sets, Zero
Dynamics, and Internal Models in the Problem of Nonlinear Output Regulation"
Dynamical generation of dark solitons in spin-orbit-coupled Bose-Einstein condensates
We numerically investigate the ground state, the Raman-driving dynamics and
the nonlinear excitations of a realized spin-orbit-coupled Bose-Einstein
condensate in a one-dimensional harmonic trap. Depending on the Raman coupling
and the interatomic interactions, three ground-state phases are identified:
stripe, plane wave and zero-momentum phases. A narrow parameter regime with
coexistence of stripe and zero-momentum or plane wave phases in real space is
found. Several sweep progresses across different phases by driving the Raman
coupling linearly in time is simulated and the non-equilibrium dynamics of the
system in these sweeps are studied. We find kinds of nonlinear excitations,
with the particular dark solitons excited in the sweep from the stripe phase to
the plane wave or zero-momentum phase within the trap. Moreover, the number and
the stability of the dark solitons can be controlled in the driving, which
provide a direct and easy way to generate dark solitons and study their
dynamics and interaction properties.Comment: 10 pages, 9 figur
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