Ground state travelling waves in infinite lattices

Abstract

In this paper, we consider FPU lattices with particles of unit mass. The dynamics of the system is described by the infinite system of second order differential equations q¨n=U'(qn+1−qn)−U'(qn−qn−1), n∈ℤ,where qn denotes the displacement of the n-th lattice site and U is the potential of interaction between two adjacent particles. Inspired by previous work due to Szulkin and Weth (Ground state solutions for some indefinite variational problems, J. Funct. Anal., 257 (2009), 3802-3822), we investigate the existence of solitary ground waves, i.e., nontrivial solutions with least possible energy.