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We consider non-linear wave type solutions with mass scale parameter andvahished canonical spin density operator in a pure SU(2) quantum chtomodynamics(QCD). A new stationary solution which can be treated as a system of staticWu-Yang monopole dressed in off-diagonal gluon field is proposed. A remarkablefeature of such a solution is that it possesses a finite energy densityeverywhere. All considered non-linear wave type solutions have common features:presence of a mass scale parameter, non-vanishing projection of the colormagnetic field along the propagation direction and zero spin density. The lastproperty requires revision of the gauge invariant definition of the spindensity operator which supposed to be massless vector field in the classicaltheory. We construct a gauge invariant definition of the classical gluon spindensity which is unique and Lorentz frame independent.

Gauge invariant gluon spin operator for spinless non-linear wave solutions