No abstract

No abstract

Applications of the Darboux transformation method to study the reduced Maxwell-Bloch (RMB) system and of the self-induced transparency (SIT) equations are considered. Both systems describe the propagation of ultrashort optical pulses in a two-level medium to a reasonable approximation. The main result of the present work is the construction of multisoliton solutions on an arbitrary background for RMB and SIT equations. Particular cases of these solutions are discussed in some detail.

No abstract

The algebraic structure of the set of solutions for the Davey-Stewartson equations is investigated. Simple and binary Darboux transforms are constructed. It is shown that the set of Darboux transforms for n auxiliary solutions of the corresponding linear Zakharov-Shabat problem comprise an Abelian group of order 2n. The Darboux technique allows nonlinear superposition formulas and dromion solutions to be obtained as in the 2+1 inverse scattering transform method. New solutions periodic in space and time for DS1 and new solutions exponentially decaying and oscillating in all directions except two (with discrete set of points on them) for DS2 are constructed. These solutions are analogues of dromions of DS1. The authors call these solutions, constructed for DS2, degenerate exultons.