The existence of Bogomolny decomposition for systems of some generalized nonlinear partial differential equations of second order

Abstract:
Using  the concept of strong necessary conditions we seek the Bogomolny decomposition for the systems of generalized hyperbolic and elliptic NPDE's of the second order. The generalization means variable equation coefficients depending on the field variables. As the results we derive the conditions for the existence of the Bogomolny relationships. As an example of illustration we present a solution for the 2d static easy axis Heisenberg model.