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The coupled nonlinear Schrödinger (CNLS) system is often used to describe physical problems such as wave propagation in a birefringent optical fiber. Under investigation in this paper is the nonlocal -symmetric reverse-space type of CNLS system, through constructing two types of Darboux transformation (DT), we will derive a new series of nonlocal analytic solutions: (1) Single-periodic and double-periodic solutions; (2) Four different combinations about dark and anti-dark solitons, as well as the bright and dark breathers on a periodic background. Moreover, the fundamental properties and dynamical behaviors of those solutions will be discussed. [ABSTRACT FROM AUTHOR]

In this paper we construct Darboux transformations and Bäcklund transformations for the supersymmetric two-boson hierarchy. Three Darboux transformations and associated Bäcklund transformations are obtained. For one of them, we also work out the corresponding nonlinear superposition formula. We build, for both the supersymmetric two-boson equation and the N = 2 , a = 4 supersymmetric KdV equation, their one-soliton solutions and present their semi-discrete versions. [ABSTRACT FROM AUTHOR]