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We consider 1+3-dimensional domain wall solutions of heterotic supergravityon a six-dimensional warped nearly K\"ahler manifold $X_6$ in the presence ofgravitational and gauge instantons of tanh-kink type as constructed in[arXiv:1109.3552]. We include first order $\alpha'$ corrections to theheterotic supergravity action, which imply a non-trivial Yang-Mills sector andBianchi identity. We present a variety of solutions, depending on the choice ofinstantons, for the special case in which the SU(3) structure on $X_6$satisfies $W_1^-=0$. The solutions preserve two real supercharges, whichcorresponds to $\mathcal{N}{=}1/2$ supersymmetry from the four-dimensionalpoint of view. Besides serving as a useful framework for collecting existingsolutions, the formulation in terms of dynamic SU(3) structures utilized hereallows us to obtain new solutions in as yet unexplored corners of the instantonconfiguration space. Our approach thus offers a unified description of theembedding of tanh-kink-type instantons into half-BPS solutions of heteroticsupergravity where the internal six-dimensional manifold has a warped nearlyK\"ahler geometry

Order $\alpha'$ heterotic domain walls with warped nearly K\"ahler geometry