An infeasible projection-type algorithm for finding nonnegative ground state solutions of nonlinear Schrödinger equations

In this paper, a projected infeasible algorithm is proposed to compute the positive ground states of the nonlinear Schrödinger (NLS) equation, which can be regarded as an energy minimization problem with an orthogonal constraint. To further preserve the positivity of the ground states which is a necessary condition in some physical systems such as the non-rotating Bose–Einstein condensates, the saturable equation and the modified Gross–Pitaevskii equation, the projection is added to the infeasible method. The local Q-linearly convergence analysis of algorithm is established for the appropriate parameter values. Numerical experiments about computing the ground states of different types of the NLS equations illustrate that the proposed algorithm is efficient and faster than other feasible algorithms in dealing with large-scale problems.