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• W2201111814 abstract "We study asymptotically and numerically fundamental gaps (i.e. difference between the first excited state and the ground state) in energy and chemical potential of the Gross-Pitaevskii equation (GPE) -- nonlinear Schr{o}dinger equation (NLSE) with cubic nonlinearity -- with repulsive interaction under different trapping potentials including box potential and harmonic potential. Based on our asymptotic and numerical results, we formulate a gap conjecture on the fundamental gaps in energy and chemical potential of the GPE on bounded domains with the homogeneous Dirichlet boundary condition and in the whole space with a convex trapping potential growing at least quadratic in the far field. We extend these results to the GPE on bounded domains with either the homogeneous Neumann boundary condition or periodic boundary condition. Finally, we obtain ground state approximations and their corresponding energy and chemical potential asymptotics of the NLSE with general nonlinearity and different trapping potentials for different parameter regimes and observe bifurcations in the ground states when the power of the nonlinearity goes to $infty$. Numerical results are reported to support the asymptotic results." @default.
• W2201111814 created "2016-06-24" @default.
• W2201111814 creator A5064750893 @default.
• W2201111814 creator A5076698229 @default.
• W2201111814 date "2015-12-22" @default.
• W2201111814 modified "2023-09-27" @default.
• W2201111814 title "Fundamental gaps and energy asymptotics of the Gross-Pitaevskii/Nonlinear Schrodinger equation with repulsive interaction" @default.
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• W2201111814 hasPublicationYear "2015" @default.
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