We present results of our research on a multiple-pulse operation of passive mode-locked fiber lasers. The research has been performed on basis of numerical simulation. Multihysteresis dependence of both an intracavity energy and peak intensities of intracavity ultrashort pulses on pump power is found. It is shown that the change of a number of ultrashort pulses in a laser cavity can be realized by hard as well as soft regimes of an excitation and an annihilation of new solitons. Bound steady states of interacting solitons are studied for various mechanisms of nonlinear losses shaping ultrashort pulses. Possibility of coding of information on basis of soliton trains with various bonds between neighboring pulses is discussed. The role of dispersive wave emitted by solitons because of lumped intracavity elements in a formation of powerful soliton wings is analyzed. It is found that such powerful wings result in large bounding energies of interacting solitons in steady states. Various problems of a soliton interaction in passive mode-locked fiber lasers are discussed. 1. Introduction Lasers generating ultrashort optical pulses are widely employed in diversified areas of science, technology, and engineering [1–7]. Applications of such lasers range from testing of ultrahigh speed semiconductor devices to precision processing of materials, from triggering of tracing chemical reactions to sophisticated surgical applications in medicine. These lasers are used for study of ultrahigh speed processes in atomic and molecular physics, in solid-state physics, and in chemistry and biology. They are employed for investigation of light-matter interactions under ultrahigh intensity levels. Lasers of ultrashort optical pulse with a high repetition rate are a key element in high-speed optical communications. Ultrashort pulse lasers are extensively used for micromachining, biomedical diagnostic, in light detection, and ranging (lidar) systems, and so forth. The great diversity of applications of ultrashort pulse lasers calls for further development and perfection of this type of quantum generators. At the present time, one of main ways for creation of perfect ultrashort pulse sources is related to passive mode-locked fiber lasers [8–16]. Nonlinear losses forming ultrashort pulses in fiber lasers are usually realized by the nonlinear polarization rotation technique. These lasers have unique potentialities. They are reliable, compact, flexible, and of low cost. Such generators can be conveniently pumped with commercially available semiconductor lasers. The nonlinear losses
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