Effect of frequency detunings and finite relaxation rates on laser localized structures

We study, analytically and numerically, the effect of frequency detunings a nd relaxation processes in laser media on stability and bifurcations of dis sipative optical localized structures (DOLS's) in a transversely one-dimens ional laser with a saturable absorber. The approximate envelope equation, w ith an intensity dependent effective coefficient of the diffusion, is deriv ed. Andronov-Hopf bifurcarions resulting from frequency detuning and leadin g to oscillatory DOLS's are analyzed numerically. A numerical and analytica l study of bifurcations of transversely motionless DOLS's in a laser with f inite relaxation rates of amplifying and absorbing media is performed. New types of DOLS's are found, including those moving with a large transverse v elocity and those moving with a periodically oscillating transverse velocit y. Hysteresis between different types of DOLS's is demonstrated.