TY - JOUR
T1 - Ground States and Energy Asymptotics of the Nonlinear Schrödinger Equation with a General Power Nonlinearity
AU - Xinran Ruan & Wenfan Yi
JO - Communications in Computational Physics
VL - 4
SP - 1121
EP - 1142
PY - 2018
DA - 2018/06
SN - 24
DO - http://doi.org/10.4208/cicp.2018.hh80.02
UR - https://global-sci.org/intro/article_detail/cicp/12321.html
KW - Nonlinear Schrödinger equation, ground state, energy asymptotics, repulsive interaction.
AB - <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>