Conservation laws, bilinear Bäcklund transformations and solitons for a nonautonomous nonlinear Schrödinger equation with external potentials

摘要: Abstract Under investigation in this paper is a nonautonomous nonlinear Schrodinger equation with external potentials, which can govern the dynamics of solitons optical medium non-uniformly distributed both transverse and longitudinal directions. Based on Lax pair, we present an infinite sequence conservation laws. Bilinear forms, bilinear Backlund transformations, one-, two- N-soliton solutions under known variable-coefficient constraint are generated via Hirota method. With G ( t ) = 0 R B being constant, amplitude soliton remains unvarying during propagation, where scaled time, G(t) gain/loss coefficient, B(t), group velocity dispersion R(t), nonlinearity coefficient. If set ≠ or as variable, becomes varying. Due to different choices linear oscillator potential coefficient α(t), periodic-, parabolic-, S- V-type observed. Meanwhile, find that α(t) has no influence amplitude. Interaction between two amplitude-unvarying amplitude-varying ones displayed, respectively. The moving always keeps