On transverse stability of discrete line solitons

We obtain sharp criteria for transverse stability and instability of line solitons in the discrete nonlinear Schrödinger equations on one- and two-dimensional lattices near the anti-continuum limit. On a two-dimensional lattice, the fundamental line soliton is proved to be transversely stable (unstable) when it bifurcates from the X (Γ) point of the dispersion surface. On a one-dimensional (stripe) lattice, the fundamental line soliton is …