Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation

Rogue waves are a class of nonlinear waves with extreme amplitudes, which usually appear suddenly and disappear without any trace. Recently, the parity-time ($\mathcal {PT}$)-symmetric vector rogue waves (RWs) of multi-component nonlinear Schrödinger equation ($n$-NLSE) are usually derived by the methods of integrable systems. In this paper, we utilize the multi-stage physics-informed neural networks (MS-PINNs) algorithm to derive the data-driven $\mathcal {PT}$ symmetric vector RWs solution of coupled NLS system in elliptic and X-shapes domains with nonzero boundary condition. The results of the experiment show that the multi-stage physics-informed neural networks are quite feasible and effective for multi-component nonlinear physical systems in the above domains and boundary conditions.     

New Rogue Wave Solutions of (1+2)-Dimensional Non-Isospectral KP-II Equation

The generalized binary Darboux transformation for the (1+2)-dimensional non-isospectral KP-II equation is presented. Moreover, as a direct application, the new rogue wave solutions for the (1+2)-dimensional non-isospectral KP-II equation are constructed by the generalized binary Darboux transformation.