A Mel'nikov approach to soliton-like solutions of systems of discretized nonlinear Schrödinger equations

DOI10.1016/S0167-2789(97)84201-7zbMath0938.37035MaRDI QIDQ1963416

Michael Kollmann, Tassos C. Bountis

Publication date: 1 February 2000

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

Mel'nikov analysissymplectic mapnonlinear latticediscretized nonlinear Schrödinger equationshomoclinic orhitsintegrable Ablowitz-Ladik differential-difference equationssoliton-like time-periodic states

Mathematics Subject Classification ID

Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Discrete version of topics in analysis (39A12) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60)

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Cites Work

• The discrete self-trapping equation
• Nonlinear equations in the applied sciences
• Optical switching in three-coupler configurations
• Exponentially small splitting of separatrices for perturbed integrable standard-like maps
• Integrable mappings and soliton equations. II
• Anti-integrability in dynamical and variational problems
• A Mel'nikov vector for \(N\)-dimensional mappings
• Nonlinear differential–difference equations and Fourier analysis
• Mel’nikov’s Function for Two-Dimensional Mappings