Two-Dimensional Lorentz-Invariant Field Theory Models with Higher Integrals of Motion. 1: Complex Scalar Fields

摘要

All the Lagrange Lorentz invariant field theory models in two dimensional space time for the complex scalar fields with the quadratic in field gradients lagrangian which possess an infinite set of local conserved currents that are polynomial in field derivatives were found. All these models are integrable by the inverse scattering method. It is shown that only two nontrivial essentially different models of this type exist for massive fields (complex sine-Gordon-I and II'').