| Abstract: |
| We utilize an inverse scattering transform, first proposed by Bilman and Miller, to analyse solutions of the Sine-Gordon equation corresponding to spectral data consisting of purely imaginary conjugate poles of order n. Starting from zero background, the multiple-pole solitons are constructed by n-fold applications of Darboux transformations. The inverse scattering transform yields Riemann-Hilbert problem representations of these structures which, under appropriate scaling, reveal regions of oscillation and attenuation. The boundaries of the attenuated regions can be computed exactly, which allows nonlinear steepest-descent methods to yield asymptotical description of the solutions in these regions in the limit of large order. This is joint work with Deniz Bilman and Robert Buckingham. |
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