Ground States and Energy Asymptotics of the Nonlinear Schrödinger Equation with a General Power Nonlinearity (Communications in Computational Physics, 2020)
We study analytically the existence and uniqueness of the ground state ofthe nonlinear Schrödinger equation (NLSE) with a general power nonlinearity describedby 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 correspondingenergy and chemical potential in weak or strong interaction regimes with a fixednonlinearity σ. Besides, we study the case where the nonlinearity σ→∞ with a fixedinteraction strength. In particular, a bifurcation in the ground states is observed. Numericalresults in 1D and 2D will be reported to support our asymptotic results.