Structure-preserving Gauss methods for the nonlinear Schrödinger equation

We use the scalar auxiliary variable (SAV) reformulation of the nonlinear Schrodinger (NLS) equation to construct structure-preserving SAV–Gauss methods for the NLS equation, namely $$L^2$$ -conservative methods satisfying a discrete analogue of the energy (the Hamiltonian) conservation of the equation. This is in contrast to Gauss methods for the standard form of the NLS equation that are $$L^2$$ -conservative but not energy-conservative. We also discuss efficient linearizations of the new methods and their conservation properties.