  In this paper, first we introduce the notion of a Leibniz bialgebra and show
that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras and
Leibniz bialgebras are equivalent. Then we introduce the notion of a (relative)
Rota-Baxter operator on a Leibniz algebra and construct the graded Lie algebra
that characterizes relative Rota-Baxter operators as Maurer-Cartan elements. By
these structures and the twisting theory of twilled Leibniz algebras, we
further define the classical Leibniz Yang-Baxter equation, classical Leibniz
r-matrices and triangular Leibniz bialgebras. Finally, we construct solutions
of the classical Leibniz Yang-Baxter equation using relative Rota-Baxter
operators and Leibniz-dendriform algebras.
