  We present a new multisymplectic framework for second-order classical field
theories which is based on an extension of the unified Lagrangian-Hamiltonian
formalism to these kinds of systems. This model provides a straightforward and
simple way to define the Poincar\'e-Cartan form and clarifies the construction
of the Legendre map (univocally obtained as a consequence of the constraint
algorithm). Likewise, it removes the undesirable arbitrariness in the solutions
to the field equations, which are analyzed in-depth, and written in terms of
holonomic sections and multivector fields. Our treatment therefore completes
previous attempt to achieve this aim. The formulation is applied to describing
some physical examples; in particular, to giving another alternative
multisymplectic description of the Korteweg-de Vries equation.
