Abstract:

In this paper, we consider one dimensional FPU type lattices with particles of unit mass. The dynamics of the system is described by the following $\ddot{q}_n= U'(q_{n+1}-q_n)-U'(q_n-q_{n-1}), \quad n\in{\mathbb Z}, $ where U is the potential of interaction between two adjacent particles and q_n denotes the displacement. By directly using the usual variational method, we study the existence of ground state travelling waves, i.e., non-trivial travelling waves with least possible energy, for the above system with more general superquadratic potentials than the previous work of Pankov[10] and Zhang and Ma [20]. Moreover, we also concern the monotonicity of the solitary ground state travelling waves.

Key words: Lattice dynamical systems, Ground state travelling waves, Periodic, Solitary, Superquadratic