Soliton solutions are constructed numerically for the problem of propagation of a femtosecond pulse in a medium with a cubic nonlinearity. The problem is posed as an eigenvalue problem with an operator nonlinear in the eigenfunctions. For given values of the propagation parameter we find the real eigenvalue ~, and the corresponding eigenvector. This eigenvector is a soliton, i.e., a solution that does not vary in the coordinate of propagation of the light pulse. An algorithm is proposed to find the minimum eigenvalue and the corresponding eigenfunctions that satisfy given conditions.

A study was carried out on the reversible decomposition of dibromobromate anions in organic solvents and we found the equilibrium constants for the processes responsible for the distribution of active halogen and hydrogen halide between their different forms in solution. The capacity of the solvent to form hydrogen bonds with the bromide anion, the feasibility of forming a molecular complex with bromine, and the structure of the cation (in solutions with low ionizing capacity) were all found to affect the reversible decomposition of the dibromobromate anion.Organic salts with the dibromobromate anion, Br 3 − , have a set of unique properties, which open the way for their use in a very broad variety of applications [1]. The vapor pressure of bromine above solid crystalline dibromobromates is very low. Many of these salts are suitable for prolonged storage and safe for handling. Numerous studies have shown that the applicability of dibromobromates as electrolyte components for chemical power sources and materials for water purification, brominating agents differing from elemental bromine in their reaction mechanism [2, 3]. The profound differences in the reaction mechanisms of dibromobromates and bromine are seen in differing kinetic behavior, smaller reactivity and greater selectivity in the dibromobromate reactions [4][5][6]. However, there is a special feature in the behavior of dibromobromate solutions, which can cancel out all their advantages relative to molecular bromine. These complexes are capable of reversible dissociation in solution to give bromide anion and molecular bromine [1]. The state of these complexes has been studied in greatest detail for aqueous solution [1, 7-9]. There have been fewer measurements for solutions in organic solvents. Such measurements have far from always been the major concern in these studies. This perhaps accounts for the circumstance that determinations of equilibrium constants and even extinction coefficients do not always agree with one another. The formation of dibromobromates from bromide anion and bromine molecules may reliably be considered to be an exothermal [9], rapid [10] and equilibrium [1] reaction. The equilibrium constants vary in a very broad range depending on the solvent [11]. We can clearly imagine that the concentration of molecular bromine in the case of considerable dissociation of the dibromobromate anion becomes sufficient so that the contribution of the reaction involving bromine, which is much more reactive in many bromination reactions [3][4][5], becomes predominant. The advantages of using dibromobromates in this case would be eliminated. Hence, knowledge of the state of dibromobromate anions in solution is important for the application of these salts. We previously proposed bis(N,N-dimethylacetamide) hydrogen dibromobromate for use as an efficient brominating agent and component in compositions for the decomposition of toxic pollutants [12]. Not only the anion but also the cation is complex in this compound, which introduces additional complexit...