The existence of Bogomolny decomposition by means of strong necessary conditions
K. Sokalski, Lslash Stepie nacute, D. Sokalska · Journal of Physics A Mathematical and General · 2002
The concept of strong necessary conditions for the extremum of a functional to exist, has been applied to analyse the existence of the Bogomolny decomposition for a system of two coupled nonlinear partial differential equations in 1 + 1 dimensions. A general condition for a derivativeless term has been derived for both hyperbolic and elliptic systems. In the case of independent equations the Bogomolny equations become Bäcklund transformations. Illustrative examples are presented for the particular form of derivativeless terms.