Variational approach to the problem of dark-soliton generation

Abstract

The creation of dark solitons from an arbitrary initial pulse in the system, described by the nonlinear Schr\odinger equation, is considered by applying the variational method to the corresponding linear spectral problem. The initial pulse is a potential in the linear operator of the Zakharov-Shabat eigenvalue problem and the discrete spectrum of the problem determines the number and parameters of emerged solitons. The procedure for calculation of approximate values of the lowest- and higher-order discrete eigenvalues from spectral data of known (trial) potential is proposed. The application of this procedure to some examples shows qualitative agreement between variational and exact results.