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In this research we obtain the classical r-matrices of real two and threedimensional Jacobi-Lie bialgebras. In this way, we classify all non-isomorphicreal two and three dimensional coboundary Jacobi-Lie bialgebras and their types(triangular and quasitriangular). Also, we obtain the generalized Sklyaninbracket formula by use of which, we calculate the Jacobi structures on therelated Jacobi-Lie groups. Finally, we present a new method for constructingclassical integrable systems using coboundary Jacobi-Lie bialgebras.

Classical r-matrices of real low-dimensional Jacobi-Lie bialgebras and their Jacobi-Lie groups