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Efficient time integration methods for Gross-Pitaevskii equations with rotation term. (English) Zbl 1434.35175

Summary: The objective of this work is the introduction and investigation of favourable time integration methods for the Gross-Pitaevskii equation with rotation term. Employing a reformulation in rotating Lagrangian coordinates, the equation takes the form of a nonlinear Schrödinger equation involving a space-time-dependent potential. A natural approach that combines commutator-free quasi-Magnus exponential integrators with operator splitting methods and Fourier spectral space discretisations is proposed. Furthermore, the special structure of the Hamilton operator permits the design of specifically tailored schemes. Numerical experiments confirm the good performance of the resulting exponential integrators.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
65L20 Stability and convergence of numerical methods for ordinary differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65T50 Numerical methods for discrete and fast Fourier transforms
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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