@Article{CiCP-24-1121, author = {}, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2018.hh80.02}, url = {http://global-sci.org/intro/article_detail/cicp/12321.html} }