Drinfel'd-Sokolov construction and exact solutions of vector modified KdV hierarchy

Panagiota Adamopoulou, Georgios Papamikos

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Abstract

We construct the hierarchy of a multi-component generalisation of modified KdV equation and find exact solutions to its associated members. The construction of the hierarchy and its conservation laws is based on the Drinfel'd-Sokolov scheme, however, in our case the Lax operator contains a constant non-regular element of the underlying Lie algebra. We also derive the associated recursion operator of the hierarchy using the symmetry structure of the Lax operators. Finally, using the rational dressing method we obtain the one soliton solution and we find the one breather solution of general rank in terms of determinants.
Original languageEnglish
Article number114933
JournalNuclear Physics B
Volume952
Early online date21 Jan 2020
DOIs
Publication statusPublished - Mar 2020

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