Asymptotic analysis of breather modes in a two-dimensional mechanical lattice

摘要: Abstract We consider a two-dimensional square lattice in which each node is restricted to the plane of lattice, but permitted move both directions lattice. assume nodes are connected nearest neighbours along with nonlinear springs, and diagonal linear springs. generalised Klein–Gordon system, that is, where there an onsite potential at addition (nonlinear) nearest-neighbour interactions. derive equations motion for displacements from Hamiltonian. use asymptotic techniques form small amplitude breather solutions, find necessary conditions required their existence. two types mode, we term ‘optical’ ‘acoustic’, based on analysis other lattices support dispersion relations multiple branches. In usual inequality sign nonlinearity order NLS be focusing type, obtain additional ellipticity constraint, restriction wavenumber space, spatial differential operator elliptic.