Soliton management in the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain
The novel stable “soliton islands” in a “sea of solitary waves” of the nonlinear Schrodinger equation model with varying dispersion, nonlinearity, and gain or absorption are discovered. Different soliton management regimes are predicted.
Compact differencing can deliver high-order accuracy using only a limited span of stencils, but incurring a costly matrix in version. Hence, use of a stable implicit time discretizaton becomes favorable in order to offset the computation cost by allowing a large time step. A practical way to reduce the burden of inverting a large matrix from multidimensional problems is to split the implicit operator into a series of smaller operators. Undesirable consequences can surface, such as (1) loss of stability, and/or (2) loss of accuracy. Here, we propose a consistent implicit compact method and study the stability and accuracy of steady and unsteady solutions.