Heteroclinic standing waves in defocusing DNLS equations: variational approach via energy minimization

DOI10.1080/00036811.2010.492504zbMath1205.37084arXiv1002.1591OpenAlexW2094739385WikidataQ58149003 ScholiaQ58149003MaRDI QIDQ3163654

Michael Herrmann

Publication date: 26 October 2010

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.1591

zbMATH Keywords

variational methodsdark solitonsdiscrete nonlinear Schrödinger equation (DNLS)nonlinear lattice wavesheteroclinic standing waves

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Waves and radiation in optics and electromagnetic theory (78A40) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Lattice dynamics; integrable lattice equations (37K60)

Related Items (3)

OSCILLATORY WAVES IN DISCRETE SCALAR CONSERVATION LAWS ⋮ Ground states in spatially discrete non-linear Schrödinger models ⋮ Gauge fields, strings, solitons, anomalies, and the speed of life

Cites Work

• Existence of breather solutions of the DNLS equations with unbounded potentials
• The discrete nonlinear Schrödinger equation. Mathematical analysis, numerical computations and physical perspectives
• Breathers in nonlinear lattices: existence, linear stability and quantization
• Bifurcations of travelling wave solutions in the discrete NLS equations
• On localized solutions of discrete nonlinear Schrödinger equation: an exact result
• Gap solitons in periodic discrete nonlinear Schrödinger equations. II: A generalized Nehari manifold approach
• Periodic and decaying solutions in discrete nonlinear Schrödinger with saturable nonlinearity
• Travelling waves of discrete nonlinear Schrödinger equations with nonlocal interactions
• Global well-posedness for discrete non-linear Schrödinger equation
• Standing wave solutions of the discrete non-linear Schrödinger equations with unbounded potentials, II
• Experimental Results Related to DNLS Equations
• Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
• Gap solitons in periodic discrete nonlinear Schrödinger equations
• On some discrete variational problems

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