title: Numerical solution of the nonlinear Schrödinger equation with wave operator on unbounded domains.
abstract: In this paper, we generalize the unified approach proposed in Zhang et al. [J. Zhang, Z. Xu, and X. Wu, Phys. Rev. E 78, 026709 (2008)] to design the nonlinear local absorbing boundary conditions (LABCs) for the nonlinear Schrödinger equation with wave operator on unbounded domains. In fact, based on the methodology underlying the unified approach, we first split the original equation into two parts-the linear equation and the nonlinear equation-then achieve a one-way operator to approximate the linear equation to make the wave outgoing, and finally combine the one-way operator with the nonlinear equation to achieve the nonlinear LABCs. The stability of the equation with the nonlinear LABCs is also analyzed by introducing some auxiliary variables, and some numerical examples are presented to verify the accuracy and effectiveness of our proposed method.
authors.affiliation: School of Mathematical Sciences, Shandong Normal University, Jinan, 250014 People's Republic of China.
authors.forename: Hongwei
authors.initials: H
authors.lastname: Li
authors.affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, People's Republic of China.
authors.forename: Xiaonan
authors.initials: X
authors.lastname: Wu
authors.affiliation: Beijing Computational Science Research Center, Beijing 100084, People's Republic of China.
authors.forename: Jiwei
authors.initials: J
authors.lastname: Zhang
mesh_terms: D017711:Nonlinear Dynamics; D011789:Quantum Theory