Solitary waves in the Ablowitz–Ladik equation with power-law nonlinearity

DOI10.1088/1751-8121/aaf755zbMath1425.35178arXiv1806.10898OpenAlexW3098701703WikidataQ62592294 ScholiaQ62592294MaRDI QIDQ5243726

Lijuan Guo, Jesús Cuevas, Panayotis G. Kevrekidis, Boris A. Malomed

Publication date: 19 November 2019

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.10898

zbMATH Keywords

variational approachdiscrete solitonsAblowitz-Ladik lattices

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators (35J87) Soliton solutions (35C08)

Related Items (5)

Configurational complexity of nonautonomous discrete one-soliton and rogue waves in Ablowitz-Ladik-Hirota waveguide ⋮ The closeness of localized structures between the Ablowitz–Ladik lattice and discrete nonlinear Schrödinger equations: Generalized AL and DNLS systems ⋮ The closeness of the Ablowitz-Ladik lattice to the discrete nonlinear Schrödinger equation ⋮ Stability of compact breathers in translationally-invariant nonlinear chains with flat dispersion bands ⋮ Generalized Ablowitz-Ladik equation with a dual Lagrangian structure

Cites Work

• Unnamed Item
• On the validity of the variational approximation in discrete nonlinear Schrödinger equations
• Stability theory of solitary waves in the presence of symmetry. II
• The discrete nonlinear Schrödinger equation. Mathematical analysis, numerical computations and physical perspectives
• Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity
• Stability theory of solitary waves in the presence of symmetry. I
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Peregrine solitons and gradient catastrophes in discrete nonlinear Schrödinger systems
• Spectral and dynamical stability of nonlinear waves
• Soliton dynamics in the discrete nonlinear Schrödinger equation
• Bright and dark solitons for a discrete (2+1)-dimensional Ablowitz-Ladik equation for the nonlinear optics and Bose-Einstein condensation
• Stability of waves in discrete systems
• The Defocusing Nonlinear Schrödinger Equation
• Nonlinear differential−difference equations
• Nonlinear differential–difference equations and Fourier analysis
• Excitation thresholds for nonlinear localized modes on lattices
• Nonlinear dynamics and statistical physics of DNA
• General rogue waves in the focusing and defocusing Ablowitz–Ladik equations

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