The nonlinear Schrödinger equation (NLSE) describes a vast variety of phenomena in the optics of Kerr media. Being supplied by gain and dissipation it is employed for modeling of open systems [1,2]. Soliton formation described by the NLSE equation and soliton properties depend dramatically on the dimensionality of the system. In particular, in the conservative case, while the one-dimensional cubic NLSE equation with homogeneous coefficients has stable soliton solutions, no stable localized states can exist in two or more dimensions in focusing medium. When homogeneous linear gain and nonlinear dissipation are added to the system, stable stationary localized structures do not exist even in one-dimensional case. Nevertheless, stabilization can be achieved by considering a spatially localized gain.
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