Exact theory of localized and periodic structures in active optical   cavity
  The nonlocal order parameter equation for nonlinear optical resonator is approximated in the limit of high Fresnel number by the Swift- Hohenberg equation. The exact soliton and periodic solutions of the Swift- Hohenberg equation for optical resonator with thin slice gain element are obtained. It is shown that hyperbolic "flat" secant, "chirped" secant and Jacobi elliptic functions solutions in one transverse dimension are nonlinear eigenmodes for plane - parallel, confocal and quasiconfocal geometries. 
A.Yu.Okulov