Soliton-like oscillations of an infinite beam on a non-linearly elastic support

This article deals with travelling wave motions of a homogeneous infinite elastic beam. It is assumed that the beam lies on a dense support. The authors describe that support as an infinite set of identical springs obeying a non-linear deformation law. It has been proven that the above motions can be described by means of a Hamiltonian system of equations with two degrees of freedom. The authors use local methods of Hamiltonian mechanics and some well known results of the KAM-theory to analytically investigate the system under consideration. The authors give conditions to existence of solitary wave motions and derive their asymptotic representations. To check the analytic results, the authors fulfil certain numerical experiments. The above conditions to existence are revised with the help of the Poincare map method.