Soliton collision and reshaping of eigenvalue spectrum using local perturbation

We study collision of soliton pair in model of nonlinear Schrödinger equation. The soliton collision is disturbed by the local perturbation of the fiber dispersion. The analysis of the eigenvalues of Zakharov-Shabat spectral problem is given. Reshaping of the eigenvalue sets occur in the form of bifurcations. Peculiar features include soliton fusion into a breather and conversion of solitons at rest into a pair with outward velocities.