A numerical method for finding multiple co-existing solutions to nonlinear cooperative systems (Q952807)

The authors develop a local min-orthogonal method for solving cooperative nonlinear elliptic systems for multiple co-existing solutions. For this purpose, they establish a local min-orthogonal characterization for the coexisting critical points of dual functionals and based on this characterization they prove the convergence of the method. The authors numerically implement the method for solving two coupled nonlinear Schrödinger equations with model spatial vector solutions propagating in a saturable bulk nonlinear medium for multiple co-existing solutions.