In this paper the one-dimensional nonparaxial nonlinear Schrödinger equation is considered.
This was proposed as an alternative to the classical nonlinear Schrödinger 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.
