Multiple-Pole Solutions of the Modified Korteweg-de Vries Equation

New types of solutions of completely integrable nonlinear evolution equations are found using the inverse scattering method. For the Modified Korteweg-de Vries equation the multiple-pole solutions, i.e., the solutions which correspond to multiple-pole of the reflection coefficient are investigated. Double-pole soltuion and triple-pole solution are obtained explicitly. It is shown that those solutions describe a weak-bound state of solitons and antisolitons.

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