Conformal structure‐preserving method for two‐dimensional damped nonlinear fractional Schrödinger equation

Abstract

This paper mainly analyzes conservation laws and convergence of splitting conformal multisymplectic scheme for solving the two-dimensional damped nonlinear fractional Schrödinger equation. In order to obtain conformal multisymplectic scheme, first using Strang splitting method, the original problem is split into conservative multisymplectic and dissipative multisymplectic systems. The conservative multisymplectic system is numerically solved and the dissipative part is solved exactly. And then there shows the corresponding conservation laws and numerical scheme, in which the implicit midpoint method is used in time and the Fourier pseudospectral method is used in space, it also preserves conformal multisymplectic, the global conformal symplectic and global conformal mass conservation laws. Most important of all, we discuss convergence of the proposed scheme which is second-order accuracy in time and spectral accuracy in space. Finally, the validity and accuracy of the theoretical results are verified by several numerical examples.