Perturbations of soliton solutions to the unstable nonlinear Schrodinger and Sine-Gordon equations

摘要

The adiabatic evolution of soliton solutions to the unstable nonlinear Schrodinger (UNS) and sine-Gordon (SG) equations in the presence of small perturbations is reconsidered. The transport equations describing the evolution of the solitary wave parameters are determined by a direct multiple-scale asymptotic expansion and by phase-averaged conservation relations for an arbitrary perturbation. The evolution associated with a dissipative perturbation is explicitly determined and the first-order perturbation fields are also obtained.