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The multiple-pole soliton, periodic and rational solutions for the fifth-order modified Korteweg–de Vries equation are derived via the robust inverse scattering transform method. More specifically, the first-order spatial periodic solution and first-order, second-order rational solutions with a nonzero constant background are obtained explicitly. Furthermore, a second-order pole soliton formula is found by onefold application of Darboux transformation under the condition of zero background with associated spectral data consisting of a single pair of conjugate poles of order 2. The dynamical behaviors of these solutions are also depicted in detail.
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