Local and nonlocal currents for nonlinear equations (Q1059225)

A general method is proposed for constructing conserved currents for a large class of (multidimensional) nonlinear equations. For the nonlinear differential equations that can be represented as the solvability condition of some overdetermined linear system with a parameter (in particular, ones that can be integrated by the inverse scattering method), a procedure for the explicit calculation of the conserved currents is proposed. Examples are considered: nonlinear Dirac equation, nonlinear wave equation, Navier-Stokes equation, Boltzmann equation, nonlinear Schrödinger equation, Korteweg-de Vries equation, chiral field, Heisenberg magnet, Yang-Mills equations, supersymmetric Yang-Mills equations, and others.