Existence of solitons in infinite lattice.
We consider necessary conditions for existence of optical solitons in one-dimensional nonlinear periodic layered array. We show analytically that in the array with the cubic-quintic nonlinearity bistable solitons are possible whereas for the Kerr nonlinearity they never exist. We investigate asymptotic behavior of the soliton amplitude at infinity. With help of the asymptotic a numerical algorithm for searching the solitons may be developed so that finding a soliton on finite interval is simultaneously the numerical proof of its existence on infinite interval.
Gisin
Boris V
BV
Department of Electrical Engineering-Physical Electronics, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel.