Spatiotemporal complexity of the cubic-quintic nonlinear Schrodinger equation

The integrability of the cubic-quintic nonlinear Schrodinger equation is investigated numerically. By analytically studying the linear stability of the homogeneous state and numerically solving such a continuum Hamiltonian dynamic system, the authors show that the quintic nonlinear term leads to a spatiotemporal complexity of wave fields, and illustrate that this-behaviour is associated with the stochastic partition of energy in Fourier modes. In addition, they show the presence of the stochastic motion is due to the homoclinic orbit crossings.