Optical memory. The concept of optical memory based on long-term photon-echo (LTPE) phenomenon has been developed. Amazingly, the storage time in these devices can be as long as minutes, hours and even days. The theory of optical echo in the system of rare-earth ions with hyper-fine splitting of optical levels is quite involved. It has been predicted, for the first time, that multiple reading and selective erasing of information can be achieved in these devices. These facts open the ways for high capacity random access optical memory devices. The existence of each of these phenomena had been confirmed experimentally. Multiple echo has been found experimentally in our work [\ref{AA69}]. Experimentally the possibility of selective erasing of information has been independently confirmed by the group of Prof. Hartmann (Columbia University, USA) [see Opt.Lett., 18, 1789 (1993)] and by the group of Dr. S. Kröll in Sweden [Opt.Lett., 18, 1834 (1993)]. Further experimental research in this derection has been done in collaboration with Prof. N. Manson (LPC, ANU).

Nonlinear surface waves. Asymmetric nonlinear modes of symmetric waveguide structures have been shown to exist for the first time. This presented the possibility of bistable behaviour of waveguiding modes above a certain threshold. The work on asymmetric nonlinear modes opened possibilities for nonlinear switching phenomena in planar waveguides. The second paper related to nonlinear surface waves published in collaboration with Korneev and Kuz'menko presented stability results for nonlinear surface waves and their dynamics. The Fellowship of OSA was awarded to N.Akhmediev in 1996 for a series of works including these two.

Bifurcations of solitons. Bifurcations of solitons have been discovered in our works. The consequence of these bifurcations is the multiplicity of ground state soliton solutions in dual - or multi-component fiber devices. In presence of several branches stability of solitons of various branches becomes a critical issue. Bistability and multistability phenomena might be possible. New soliton states play an essential role in processes of soliton switching. These ideas are important for fast all-optical information processing. We have found that families of coupled (asymmetric) soliton states exist both in birefringent fibers and nonlinear fiber couplers. In the former case, a new branch of elliptically polarized solitons appears. In the latter case, the new family consists of asymmetric soliton states. Knowledge in the area of light controlling light has been summarized in our book with Dr. Ankiewicz which has been published by Chapman&Hall, London in 1997 (now Kluwer).

Modulation instability. The theory of modulation instability of continuous waves in optical fibers and in nonlinear media has been developed. The exact solution of NLSE describing modulation instability of a plane wave and its full evolution has been obtained. This is one of the basic solutions of NLSE and it has the same significance as the solution describing fundamental soliton of the nonlinear Schrodinger equation. It has also been shown that the solution describes the recurrence phenomenon. The result is important both from theoretical point of view and for applications. These fundamental results are referenced in textbooks. The generalization of these results to the (2+1) dimensional case has shown that recurrence is a basic property of modulation instability in Hamiltonian systems.

Exact solutions of the nonlinear Schrodinger equation (NLSE). An original theory of solitons and periodic solutions governed by the nonlinear Schrodinger equation (NLSE) has been developed. The method is simple but powerful. It allows us to find a multiplicity of exact solutions, including some which were previously unknown. In general, a three-parameter family of exact solutions of the NLSE can be constructed. Moreover, understanding the set of solutions of NLSE as a multiparameter family allowes one to apply similar concepts to more complicated nonintegrable systems.