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Nonlinear modes in the harmonic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric potential
We study the families of nonlinear modes described by the nonlinear Schr\"odinger equation with the $\mathcal{PT}$-symmetric harmonic potential ${x}^{2}\ensuremath{-}2i\ensuremath{\alpha}x$. The nonlinear modes found display a number of interesting features. In particular, we have observed that modes bifurcating from different eigenstates of the underlying linear problem can actually belong to the …