Harmonic maps, Baecklund-Darboux transformations and 'line solution' analogues

Harmonic maps from R2 or one-connected domain Ω subset of R2 into GL(m,C) and U(m) are treated. The GBDT version of the Baecklund-Darboux transformation is applied to the case of the harmonic maps and a new and simple algebraic procedure to construct new harmonic maps from the initial ones is given, using some methods from system theory. A new general formula on the GBDT transformations of the Sym-Tafel immersions is derived. A new class of the unitary harmonic maps with asymptotics along one line essentially different from the asymptotics in all other directions, similar in certain ways to line solutions, is obtained explicitly and studied