Shape changing (intensity redistribution) collisions of solitons in mixed coupled nonlinear Schr{\"o}dinger equations

A novel kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable $N$-coupled nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients. The corresponding soliton solutions for N=2 case are obtained by using Hirota's bilinearization method. The distinguishing feature of the mixed sign CNLS equations is that the soliton solutions can both be singular and regular. Although the general soliton solution admits singularities we present parametric conditions for which non-singular soliton propagation can occur. The multisoliton solutions and a generalization of the results to multicomponent case with arbitrary $N$ are also presented. An appealing feature of soliton collision in the present case is that all the components of a soliton can simultaneously enhance their amplitudes, which can lead to new kind of amplification process without induced noise.