  It is well known that the Laplace cascade method is an effective tool for
constructing solutions to linear equations of hyperbolic type, as well as
nonlinear equations of the Liouville type. The connection between the Laplace
method and soliton equations of hyperbolic type remains less studied. The
article shows that the Laplace cascade also has important applications in the
theory of hyperbolic equations of the soliton type. Laplace's method provides a
simple way to construct such fundamental objects related to integrability
theory as the recursion operator, the Lax pair and Dubrovin-type equations,
allowing one to find algebro-geometric solutions. As an application of this
approach, previously unknown recursion operators and Lax pairs are found for
two nonlinear integrable equations of the sine-Gordon type.
