Nonlinear dynamics of short light pulse in birefringent optical fiber

This paper is devoted to the investigation of phase portraits analysis of a vector short pulse equation describing propagation of short light pulses in birefringent optical fiber. Indeed, we introduce transformations that are helpful in decoupling this equation and following the fourth order runge-kutta scheme, we construct phase portraits of the system under interest. The analysis of the phase portrait shows that the system possesses soliton solutions and periodic solutions. We derive Hamiltonian like energy of the system and show that the system is conservative. By double integration, we construct some expressions of the solutions to the system by direct integration which differ from the solutions previously obtained in the literature by the fact that they are difficult to be expressed explicitly as functions of the phase of the wave.