Summary
We give a complete classification of the small-amplitude finite-gap solutions of the sine-Gordon (SG) equation on an interval under Dirichlet or Neumann boundary conditions. Our classification is based on an analysis of the finite-gap solutions of the boundary problems for the SG equation by means of the Schottky uniformization approach.
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Communicated by Thanasis Fokas
On leave from IPPI, Moscow, Russia
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Bobenko, A.I., Kuksin, S.B. Small-amplitude solutions of the sine-Gordon equation on an interval under dirichlet or Neumann boundary conditions. J Nonlinear Sci 5, 207–232 (1995). https://doi.org/10.1007/BF01212955
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DOI: https://doi.org/10.1007/BF01212955