Progress of Pattern Dynamics in Plasma Waves (Communications in Computational Physics, 2008)
This paper is concerned with the pattern dynamics of the generalized nonlinear Schrödinger equations (NSEs) related with various nonlinear physical problems in plasmas. Our theoretical and numerical results show that the higher-order nonlinear effects, acting as a Hamiltonian perturbation, break down the NSE integrability and lead to chaotic behaviors. Correspondingly, coherent structures are destroyed and replaced by complex patterns. Homoclinic orbit crossings in the phase space and stochastic partition of energy in Fourier modes show typical characteristics of the stochastic motion. Our investigations show that nonlinear phenomena, such as wave turbulence and laser filamentation, are associated with the homoclinic chaos. In particular, we found that the unstable manifolds W(u) possessing the hyperbolic fixed point correspond to an initial phase θ =45◦ and 225◦, and the stable manifolds W(s) correspond to θ=135◦ and 315◦.