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 stabi lity of the homogeneous state and numerically solving such a continuum Hamiltonian dynamic system, we show that the quintic nonlinear term l eads to a spatiotemporal complexity of wave fields, and illustrate tha t 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.