The existence and stability properties of solitons of the nonlinear Schrödinger equation with coupling-to-a-mean-term (NLSM) equation with an external periodic potential are investigated.
Solutions to NLSM are obtained numerically by using spectral renormalization method.
The linear and nonlinear stability properties of the numerically obtained solitons are investigated.
The fundamental solitons are found to be nonlinearly unstable in the lattice-free medium due to collapse.
Collapse is suppressed by adding a periodic lattice to NLSM system.