#5723. Symplectic schemes and symmetric schemes for nonlinear Schr?dinger equation in the case of dark solitons motion

August 2026publication date
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Journal’s subject area:
Applied Mathematics;
Computational Mathematics;
Numerical Analysis;
Engineering (all);
Theoretical Computer Science;
Computational Theory and Mathematics;
Software;
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Abstract:
In this paper, symplectic schemes and symmetric schemes are presented to simulate Nonlinear Schr?dinger Equation (NLSE) in case of dark soliton motion. Firstly, by Ablowitz-Ladik model (A-L model), the NLSE is discretized into a non-canonical Hamiltonian system. Then, different kinds of coordinate transformations can be used to standardize the non-canonical Hamiltonian system. Therefore, the symplectic schemes and symmetric schemes can be employed to simulate the solitons motion and test the preservation of the invariants of the A-L model and the conserved quantities approximations of the original NLSE.
Keywords:
Ablowitz-Ladik model; dark solitons motion; nonlinear Schr?dinger equation; symmetric schemes; Symplectic schemes

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