@Article{CiCP-24-1121,
author = {Xinran Ruan and Wenfan Yi},
title = {Ground States and Energy Asymptotics of the Nonlinear Schrödinger Equation with a General Power Nonlinearity},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {4},
pages = {1121--1142},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2018.hh80.02},
url = {http://global-sci.org/intro/article_detail/cicp/12321.html}
}