On nonparaxial nonlinear Schrodinger-type equations

[摘要] In this paper the one-dimensional nonparaxial nonlinear Schrodinger equation is considered. This was proposed as an alternative to the classical nonlinear Schrodinger equation in those situations where the assumption of paraxiality may fail. The paper contributes to the mathematical properties of the equation in a two-fold way. First, some theoretical results on linear well-posedness, Hamiltonian and multi-symplectic formulations are derived. Then we propose to take into account these properties in order to deal with the numerical approximation. In this sense, different numerical procedures that preserve the Hamiltonian and multi-symplectic structures are discussed and illustrated with numerical experiments. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2020-08-01

[效力级别]  Proceedings Paper

[关键词] Nonparaxial nonlinear Schrodinger equation;Hamiltonian formulation;Multi-symplectic structure;Geometric integration