Darboux transformation and soliton solutions for the (2+1)-dimensional nonlinear Schrödinger hierarchy with symbolic computation

In this paper, the N-fold Darboux transformation is applied to the Lax pair associated with the (2+1)-dimensional nonlinear Schrödinger hierarchy. The general explicit formula for N-soliton solution is derived in terms of Vandermonde-like determinant expression. On the zero background, two different families of soliton solutions (multi-line soliton and multi-parabola soliton solutions) are constructed by applying the Darboux transformation successively. Based on the figures for several sample solutions, the soliton interactions are discussed by virtue of the physical parameters (amplitude, velocity and direction) of the interacting solitons.