General soliton solutions in a coupled (2 + 1)-dimensional wave system

The Author introduce an equation named matrix Dirac equation which can be considered as a generalization of the Dirac equation for an electron. The liaison between matrix Dirac equation and the standard Dirac equation is discussed. The Author write a Lagrangian from which matrix Dirac equation can be derived. This Lagrangian is invariant under global unitary transformations of variables. The requirement of a local invariance of Lagrangian leads to a Lagrangian with gauge fields