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arXiv · 1910.11864

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

Ross Parker·P. G. Kevrekidis·Björn Sandstede
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Abstract

In the present work, we consider the existence and spectral stability of multi-pulse solutions in Hamiltonian lattice systems. 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 $m$-pulse structures and subsequently develop a reduced matrix allowing us to address their spectral stability. As a prototypical example for the manifestation of the details of the formulation, we consider the discrete nonlinear Schr\"{o}dinger equation. 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.

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Ross Parker, P. G. Kevrekidis, Björn Sandstede. 2019-10-25. Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems. https://doi.org/10.1016/j.physd.2020.132414

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