Have a look at : https://au.mathworks.com/matlabcentral/fileexchange/49163-numerical-solution-of-1d-time-independent-schrodinger-equation-using-finite-difference-method
In order to simulate such systems of equations, you need linearization or discretization. You cannot simulate nonlinear systems directly, other than approximation, linearization, discretization etc. Some more clues :: http://cobweb.cs.uga.edu/~thiab/NLS_2.pdfhttp://www.scholarpedia.org/article/Nonlinear_Schrodinger_systems:_continuous_and_discrete etc.