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Perturbations of Soliton Solutions to the Unstable Nonlinear Schrödinger and Sine-Gordon Equations

18 Pages Posted: 11 Dec 2007  

Gordon E. Swaters

affiliation not provided to SSRN

Abstract

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.

Suggested Citation

Swaters, Gordon E., Perturbations of Soliton Solutions to the Unstable Nonlinear Schrödinger and Sine-Gordon Equations. Studies in Applied Mathematics, Vol. 118, Issue 2, pp. 99-116, February 2007. Available at SSRN: https://ssrn.com/abstract=1067205 or http://dx.doi.org/10.1111/j.1467-9590.2007.00365.x

Gordon E. Swaters (Contact Author)

affiliation not provided to SSRN

No Address Available

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