Novel Soliton Solutions of the Nonlinear Schrödinger Equation Model

The methodology developed provides for a systematic way to find an infinite number of the novel stable bright and dark “soliton islands” in a “sea of solitary waves” of the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain or absorption. It is shown that solitons exist only under certain conditions and the parameter functions describing dispersion, nonlinearity, and gain or absorption inhomogeneities cannot be chosen independently. Fundamental soliton management regimes are discovered.