Explicit soliton for the Laplacian co-flow on a solvmanifold

We apply the general Ansatz proposed by Lauret (Rend Semin Mat Torino 74:55-93, 2016) for the Laplacian co-flow of invariant G(2)-structures on a Lie group, finding an explicit soliton on a particular almost Abelian 7-manifold. Our methods and the example itself are different from those presented by Bagaglini and Fino (Ann Mat Pura Appl 197(6):1855-1873, 2018).