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, we 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, we show the presence of the stochastic motion is due to the homoclinic orbit crossings.