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Existence, Stability & Dynamics of Nonlinear Modes in a 2d Partially $\mathcal{PT}$ Symmetric Potential (1701.00553v1)
Published 2 Jan 2017 in nlin.PS
Abstract: It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when the parity symmetry condition is relaxed so that the potential is invariant under reflection in only a single spatial direction. We examine the existence, stability and dynamical properties of localized modes within the cubic nonlinear Schr\"odinger equation in such a scenario of partially $\mathcal{PT}$-symmetric potential.