We consider LieG-valued Yang-Mills fields on the space \documentclass[12pt]{minimal}
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\begin{document}$$ \mathbb{R} \times {{G} \left/ {H} \right.} $$\end{document}, where G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifold \documentclass[12pt]{minimal}
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\begin{document}$$ \mathbb{R} \times {{G} \left/ {H} \right.} $$\end{document} carries a G2-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on \documentclass[12pt]{minimal}
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\begin{document}$$ \mathbb{R} \times {{G} \left/ {H} \right.} $$\end{document} is reduced to Newtonian mechanics of a particle moving in \documentclass[12pt]{minimal}
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\begin{document}$$ {\mathbb{R}^6} $$\end{document}, \documentclass[12pt]{minimal}
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\begin{document}$$ {\mathbb{R}^4} $$\end{document} or \documentclass[12pt]{minimal}
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\begin{document}$$ {\mathbb{R}^2} $$\end{document} under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/ U(1)×U(1), Sp(2)/ Sp(1)×U(1) or G2/SU(3), respectively. We analyze all critical points and present analytical and numerical kink-and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S1×G/H and dyons on \documentclass[12pt]{minimal}
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\begin{document}$$ i\mathbb{R} \times {{G} \left/ {H} \right.} $$\end{document} are also given.
