Volume 24, Issue 4
Ground States and Energy Asymptotics of the Nonlinear Schrödinger Equation with a General Power Nonlinearity

Xinran Ruan and Wenfan Yi

10.4208/cicp.2018.hh80.02

Commun. Comput. Phys., 24 (2018), pp. 1121-1142.

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  • 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.

  • History

Published online: 2018-06

  • AMS Subject Headings

35B40, 35P30, 35Q55, 65N25

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