Integrable model of Yang–Mills theory with scalar field and quasi-instantons

Within the framework of the Euclidean conformal invariant Yang–Mills theory with a scalar field, a two-dimensional Hamiltonian system is considered which is integrable under the definite relationship between coupling constants. A particular solution of the Hamilton–Jacobi equation leads to the system of first order equations providing nonself-dual instanton-like solution of the model considered. As a generalization of the system, the quasi-self-duality equation is suggested which is integrated by means of 't Hooft ansatz and results in quas-self-dual instantons – quasi-instantons.