Integrable turbulence and statistical characteristics of chaotic wave field in the Kundu-Eckhaus equation

Integrable turbulence, as an irregular behavior in dynamic systems, has attracted a lot of attention in integrable and Hamiltonian systems. This article focuses on the studies of integrable turbulence phenomena of the Kundu-Eckhaus (KE) equation as well as the generation of rogue waves from the numerical and statistical viewpoints. First, via the Fourier collocation method, we obtain the spectral portraits of different analytical solutions. …