Bright and dark solitary waves in Kerr medium with higher order linear and nonlinear dispersions

The existence of both bright and dark solitary wave solutions has been demonstrated for higher order nonlinear Schrodinger (HNLS) equation containing up to the fourth order linear and the second order nonlinear dispersion. We found that the solutions axe completely characterized by the material properties and free from arbitrary parameters in contrast to solutions of the pure NLS equation. The two types of solution were further shown to have complementary parameter space and share a singularity line of asymptotic values oo for the solitary envelope velocities.