TY - JOUR

T1 - Drinfel'd-Sokolov construction and exact solutions of vector modified KdV hierarchy

AU - Adamopoulou, Panagiota

AU - Papamikos, Georgios

PY - 2020/3

Y1 - 2020/3

N2 - 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.

AB - 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.

U2 - 10.1016/j.nuclphysb.2020.114933

DO - 10.1016/j.nuclphysb.2020.114933

M3 - Article

VL - 952

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

M1 - 114933

ER -