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Perturbations of Soliton Solutions to the Unstable Nonlinear Schrödinger and Sine‐Gordon Equations
Author(s) -
Swaters Gordon E.
Publication year - 2007
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2007.00365.x
Subject(s) - dissipative system , perturbation (astronomy) , nonlinear system , adiabatic process , soliton , dissipative soliton , sine , physics , sine gordon equation , classical mechanics , mathematical physics , traveling wave , mathematical analysis , mathematics , quantum mechanics , geometry
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.