Dark-dark and bright-dark solitons for a (2+1)-dimensional variable-coefficient nonlinear Schrodinger system in a graded-index waveguide

摘要

In this letter, we study a (2 + 1)-dimensional variable-coefficient nonlinear Schrodinger system, which describes an optical beam inside the two-dimensional graded-index waveguide with polarization effects. Through the Kadomtsev-Petviashvili hierarchy reduction, the N dark-dark soliton and N bright-dark soliton solutions in terms of the Gramian are obtained, where N is a positive integer. We analyze the interaction and propagation of the dark-dark solitons graphically. With the different values of the diffraction coefficient beta(t), periodic-, cubic- and parabolic-shaped dark-dark solitons are derived. With the different values of the gain/loss coefficient gamma(t), periodic- and arctangent-profile background waves are obtained. Moreover, we discuss the effects from the dimensionless beam width omega(t), beta(t) and gamma(t) on the solitons and background waves: Shapes of the solitons are affected by omega(t) and beta(t), while profiles of the background waves are affected by omega(t) and gamma(t).