Abstract
On the basis of the non-zero boundary condition to the AB system, we derive the asymptotic Lax pair and study its spectral analysis, from which we obtain the properties of the modified Jost functions including the analyticity, asymptotic behavior and symmetric relation, and construct the corresponding Riemann-Hilbert problem. The potentials can be reconstructed according to the asymptotic expansion of the sectional analytic function and the Plemelj formulae. As an application, we study the reflectionless case of the AB system and obtain its breather solutions with some figures showing the dynamic behaviors.
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