Extremely high degree of N-soliton pulse compression in an optical fiber

A number of papers1-3 deal with the problem of multisoliton pulse self-compression in an optical fiber. Mathematically speaking theproblem reduces to seeking for the evolution of N-soliton solution of the nonlinear Schrodinger equation (NLS) for a given initial condition. In the fiber the pulse envelope ψ obeys: where ξ is a dimensionless longitudinal coordinate and τ is a dimensionless retarded time variable. Because of the early work of Satsuma and Yajima4 the solution of the problem with initial condition has been studied extensively. This is the most simple and convenient form of initial conditions but not the best one if we wish to have the maximum degree of compression.