Thirring solitons in the presence of dispersion

The effect of dispersion on existence of solitons is studied for the generalized massive Thirring model describing a nonlinear optical fiber with grating or parallel-coupled planar waveguides with misaligned axes. The Thirring solitons existing at zero dispersion are shown numerically to be separated by a finite dispersion gap from three isolated soliton branches. Inside the gap, there is an infinity of multi-soliton branches, which are presumably dynamically unstable. Thus, the Thirring solitons are structurally unstable. In another parameter region (far from the Thirring limit), solitons exist everywhere.