Abstract
In this work, we study the discrete modified Korteweg–de Vries equation under nonzero boundary conditions with the help of the robust inverse scattering transform. Starting from its Lax pair, we first present the Jost solutions, scattering matrix and their three properties. Then we construct the Riemann–Hilbert problems and Darboux matrix based on the robust inverse scattering transform, further on, rational solutions are deduced and some prominent characteristics of these solutions graphicly in detail are exhibited by choosing suitable parameters. Our results are useful to explain the related nonlinear wave phenomena.
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