A Bäcklund transformation(BT) and a recurrence formula are derived by the homogeneous balance(HB) method. A initial problem of Burgers equations is reduced to a initial problem of heat equation by the BT, the initial problem of heat equation is resolved by the Fourier transformation method, substituting various solutions of the initial problem of the heat equation will yield solutions of the in...

Abstract We determine the 6-dimensional nilpotent metric Lie algebras such that algebra $${\mathfrak {n}}$$ n has a descending series of ideals invariant under all automorphisms and dimension consecutive members decreases by one. call them having framing determined ideals. classify isometry equivalence classe...