| Abstract: |
| The focusing integrable discrete nonlinear Schroedinger equation can be solved by inverse scattering. In the reflectionless case, it admits a (multi-)soliton solution under generic assumptions. Phase shifts are determined by the eigenvalues. We consider what happens if the reflection coefficient does not vanish identically. The soliton resolution conjecture is valid. Namely, the
solution is asymptotically a sum of 1-solitons. If |n/t| is less than 2, the phase shifts depend on the eigenvalues and the reflection coefficient. If |n/t| is not less than 2, they are independent of the reflection coefficient. Details
can be found in arXiv:1512.01760 [math-ph] |
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