Three-magnon problem and integrability of rung-dimerized spin ladders

Integrability problem for rung-dimerized spin ladder is studied by coordinate Bethe Ansatz method in three-magnon sector. It is shown that solvability of the three-magnon problem takes place for the same values of coupling constants in the Hamiltonian which guaranty solvability of the Yang–Baxter equation for the corresponding $R$-matrix. Bibl. – 15 titles.