Year: 2026
Type: article
Abstract: . We study the discrete nonlinear Schrödinger equation with competing powers [Formula: see text] satisfying [Formula: see text]. The physically relevant cases are given by [Formula: see text], [Formula: see text], and [Formula: see text]. In the anticontinuum limit, all intrinsic localized modes are compact and can be classified by their codes, which record one of two nonzero (smaller and larger) states and their sign alternations. By using the spectral stability analysis, we prove that the codes for larger states of the same sign are spectrally and nonlinearly (orbitally) stable, whereas the codes for smaller states of the alternating signs are spectrally stable but have eigenvalues of negative Krein signature. We also identify numerically the spectrally stable codes which consist of stacked combinations of the sign-definite larger states and the sign-alternating smaller states.
DOI: 10.1137/25m1810350
Authors: Georgy L. Alfimov, Pavel A. Korchagin, Dmitry E. Pelinovsky
Language: English
Topic: Nonlinear Photonic Systems
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416623257
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