Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems


In the present work, we consider the existence and spectral stability of multi-pulse solutions in Hamiltonian lattice systems which are invariant under a one-parameter unitary group of symmetries. We provide a general framework for the study of such wave patterns based on a discrete analogue of Lin’s method, previously used in the continuum realm. We develop explicit conditions for the existence of multi-pulse standing wave structures and subsequently develop a reduced matrix allowing us to address their spectral stability. As a prototypical example, we consider the discrete nonlinear Schrödinger equation (DNLS). Using Lin’s method, we extend existence and linear stability results of multi-pulse solutions beyond the anti-continuum and continuum limits. Different families of 2- and 3-pulse solitary waves are discussed, and analytical expressions for the corresponding stability eigenvalues are obtained which are in very good agreement with numerical results.

Physica D 408 (2020) 132414