The local wave phenomenon in the quintic nonlinear Schrodinger equation by numerical methods

The nonlinear Schrodinger hierarchy has a wide range of applications in modeling the propagation of light pulses in optical fibers. In this paper, we focus on the integrable nonlinear Schrodinger (NLS) equation with quintic terms, which play a prominent role when the pulse duration is very short. First, we investigate the spectral signatures of the spatial Lax pair with distinct analytical solutions and their periodized wavetrains by Fourier oscillatory method. Then, we numerically simulate the wave evolution of the quintic NLS equation from different initial conditions through the symmetrical split-step Fourier method. We find many localized high-peak structures whose profiles are very similar to the analytical solutions, and we analyze the formation of rouge waves (RWs) in different cases. These results can be helpful to understand the excitation of nonlinear waves in some nonlinear fields, such as the Heisenberg ferromagnetic spin system in condensed matter physics, ultrashort pulses in nonlinear optical fibers, and so on.

Automated summary

The paper focuses on the integrable nonlinear Schrodinger equation with quintic terms, which is widely used in modeling the propagation of light pulses in optical fibers. The spectral signatures and periodized wavetrains of the spatial Lax pair are investigated analytically and numerically, and the formation of rogue waves is analyzed. The results are important for understanding the excitation of nonlinear waves in various fields.