| Abstract: |
| This talk presents recent advances in numerical computation for the action ground state (GS) of the nonlinear Schr\odinger equation with possible rotational effects. We first establish computationally feasible variational characterizations for the action GS: minimization problems with the Nehari constraint or the $L^{p+1}$-normalization for both focusing and defocusing cases, and the unconstrained action minimization specifically for the defocusing case. Then, we develop effective numerical algorithms for computing the action GS by solving these variational problems, with rigorous convergence analysis. Furthermore, by combining theoretical analysis with numerical explorations, we present results regarding the properties of the action GS, in particular revealing its non-equivalence with the energy GS. |
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