Dynamical chaos of solitons and nonlinear periodic waves

F.Kh. Abdullaev
1989 Physics reports  
Introduction 3 3.2. Dynamical chaos of breathers in the sine-Gordon 1. Methods of analysis of dynamical stochastization of non-system with parametric excitation linear waves 5 3.3. Spatial and temporal chaos in the sine-Gordon system 1.1. Direct methods of perturbation theory for solitons 6 3.4. Breather chaos in the nonlinear Schrodinger equation 1.2. Perturbation theory based on the inverse scattering with damping and amplification transform 9 3.5. Stochastic dynamics of a breather
more » ... with a 1.3. Perturbation theory for nonlinear periodic waves 11 local inhomogeneity 1.4. Methods of analysis of stochastic dynamics of finite-4. Stochastization of nonlinear periodic waves dimensional systems 14 4.1. Dynamical chaos of a cnoidal wave in a periodically 1.5. Numerical methods 17 inhomogeneous medium 2. Dynamical chaos of solitons in almost integrable and 4.2. Stochastization of soliton lattices in the perturbed SG nonintegrable systems 18 and NSE systems 2.1. Brownian motion of a soliton in a driven sine-Gordon 4.3. Stochastization of soliton lattices in radiofrequency system 19 chains and resonators 2.2. Brownian motion of a SG soliton in the fields of two 4.4. On the generation of soliton structures from noise waves or of a wave packet 21 5. Dynamical chaos of solitons in discrete systems 2.3. Stochastic dynamics of NSE solitons in a periodic 5.1. Chaos of solitons in the Toda chain potential 23 5.2. Chaotic dynamics of a nonlinear chain of coupled 2.4. Chaos of Zakharov solitons in a periodic field 27 oscillators 2.5. Soliton turbulence in the Zakharov system 29 6. Applications to condensed matter physics 2.6. Decay of the NSE soliton in a resonator with periodi-6.1. Chaos of magnetization in ferromagnets under the cally modulated boundaries 31 action of an external field 2.7. Stochastic dynamics of a three-dimensional bubble in 6.2. Chaos in long Josephson junctions a parametrically driven SG system 32 6.3. Dynamical chaos of optical solitons 2.8. Radiative effects in a fully developed chaos 35 7. Conclusion 2.9. Dynamical chaos of sine-Gordon solitons in bounded Appendix A media 37 Appendix B 3. Dynamical chaos of two-soliton systems 40 References 3.1. Dynamical chaos of a breather under the action of an external field 40 Single orders for this issue
doi:10.1016/0370-1573(89)90098-7 fatcat:r23v64jpbbeebn35g3tqmb2cxi