Abstract
An integrable equation due to Drinfel’d and Sokolov [Sov. Math. Dokl. 23, 457 (1981)] and Wilson [Phys. Lett. A 89, 332 (1982)] (DSW) is studied in detail. It is shown how this system can be obtained as a six-reduction of the Kadomtsev–Petviashvili hierarchy. This equation presents a novel type of solutions called static solitons: they are static solutions that interact with moving solitons without deformations. Examples of such solutions are given, together with a general procedure for their construction. Finally the Painlevé analysis of the DSW equation is performed directly on the bilinear form, which constitutes a new application of the singularity analysis method.
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