一类（2+1）维变系数非线性薛定谔方程的高阶怪波解、呼吸子解和多孤子解研究

In this paper, we investigate breather, rogue wave and multi-soliton solutions for a (2+1)-dimensional variable-coefficient nonlinear Schr\"{o}dinger equation. The $N$-fold Dourboux transformation of the (2+1)-dimensional variable-coefficient nonlinear Schr\"{o}dinger equation is constructed via the Lax pair, from which the multi-soliton solutions is generalized. Meanwhile, we obtain the breather and high-order rogue wave solutions of (2+1)-dimensional variable-coefficient nonlinear Schr\"{o}dinger equation by the Darboux transformation and the generalized Darboux transfotmation from exponential seed solutions. Furthermore, we plot the graph of breather, high-order rogue wave and multi-soliton solutions and discuss in detail the propagation property of those solutions, which show some interesting structures.