Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion.

One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrödinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.

Symmetric and asymmetric evaluation of the Tokamap in comparison with direct symplectic integration.

Comparing the Poincare plots of the Tokamap and the underlying Hamiltonian system reveals large differences. This stems from the particular choice of evaluation of the singular perturbations present in the system (a series of delta functions). A symmetric evaluation approach is proposed and shown to yield results that almost perfectly match the Hamiltonian system.