Ground States and Energy Asymptotics of the Nonlinear Schrödinger Equation with a General Power Nonlinearity
Year: 2018
Communications in Computational Physics, Vol. 24 (2018), Iss. 4 : pp. 1121–1142
Abstract
We study analytically the existence and uniqueness of the ground state of the nonlinear Schrödinger equation (NLSE) with a general power nonlinearity described by the power index σ≥0. For the NLSE under a box or a harmonic potential, we can derive explicitly the approximations of the ground states and their corresponding energy and chemical potential in weak or strong interaction regimes with a fixed nonlinearity σ. Besides, we study the case where the nonlinearity σ→∞ with a fixed interaction strength. In particular, a bifurcation in the ground states is observed. Numerical results in 1D and 2D will be reported to support our asymptotic results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.2018.hh80.02
Communications in Computational Physics, Vol. 24 (2018), Iss. 4 : pp. 1121–1142
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Nonlinear Schrödinger equation ground state energy asymptotics repulsive interaction.