  General nonlinear and nonparaxial dissipative complex Helmholtz equations for
magnetic and electric fields propagating in negative refractive index materials
(NIMs) are derived ab initio from Maxwell equations. In order to describe
nonconservative soliton dynamics in NIMs, such coupled equations are reduced
into generalized Ginzburg-Landau equation. Cross-compensation between the
excess of saturating nonlinearity, losses, and gain renders these
self-organized solitons dissipationless and exceptionally robust. The presence
of such solitons makes NIMs effectively dissipationless.
