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

PHYSICA D-NONLINEAR PHENOMENA

卷:408

Article

Parker, Ross¹  Kevrekidis, P. G.^2,3  Sandstede, Bjorn¹ 

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[2] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[3] Univ Oxford, Math Inst, Oxford OX2 6GG, England

关键词: Multi-pulse solutions;    Hamiltonian lattice systems;    Lattice differential equations;    Lin's method;   

DOI  :  10.1016/j.physd.2020.132414

来源: Elsevier

【 摘 要 】

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 Schrodinger 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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free