Perturbations of Soliton Solutions to the Unstable Nonlinear Schrödinger and Sine-Gordon Equations
Gordon E. Swaters
affiliation not provided to SSRN
Studies in Applied Mathematics, Vol. 118, Issue 2, pp. 99-116, February 2007
The adiabatic evolution of soliton solutions to the unstable nonlinear Schrödinger (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.
Number of Pages in PDF File: 18
Date posted: December 11, 2007
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