On a Toda lattice model with a transversal degree of freedom

A transversal degree of freedom is introduced in the Toda lattice. For different orders of magnitude of the longitudinal and transversal strains, coupled and uncoupled equations for these fields are derived in the discrete case as well as the continuum limit. Travelling wave solutions of the system are obtained and compared to numerical solutions. Standing waves, obtained by separation of variables, exhibit blow-up in finite time as well as bounded behaviour.