Gap solitons in periodic discrete nonlinear Schrödinger equations
Gap solitons in periodic discrete nonlinear Schrödinger equations
It is shown that the periodic discrete nonlinear Schrödinger equation, with cubic nonlinearity, possesses gap solutions, i.e. standing waves, with the frequency in a spectral gap, that are exponentially localized in the spatial variable. The proof is based on the linking theorem in combination with periodic approximations.