Localization and coherence in nonintegrable systems

DOI10.1016/S0167-2789(03)00220-3zbMath1051.70011arXivnlin/0306011OpenAlexW3102320140MaRDI QIDQ1407927

Alan C. Newell, Benno Rumpf

Publication date: 21 September 2003

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

Full work available at URL: https://arxiv.org/abs/nlin/0306011

zbMATH Keywords

phase spaceirreversible dynamicsstatistical asymptotic states

Mathematics Subject Classification ID

Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07)

Related Items (10)

Chaotic breathers of two types in a two-dimensional Morse lattice with an on-site harmonic potential ⋮ Emergence of rogue waves from optical turbulence ⋮ Multisolitons and stability of two hump solitons of upper cutoff mode in discrete electrical transmission line ⋮ Discrete breathers in two-dimensional nonlinear lattices ⋮ Soliton pair interaction law in parametrically driven Newtonian fluid ⋮ Kinetic description of random optical waves and anomalous thermalization of a nearly integrable wave system ⋮ Weak turbulence and collapses in the Majda--McLaughlin--Tabak equation: Fluxes in wavenumber and in amplitude space ⋮ Discrete breathers in transient processes and thermal equilibrium ⋮ Extremal entropy for a constrained probability density ⋮ Stable and metastable states and the formation and destruction of breathers in the discrete nonlinear Schrödinger equation

Cites Work

• Focusing: A mechanism for instability of nonlinear finite difference equations
• Grid resonances, focusing and Benjamin-Feir instabilities in leapfrog time discretizations
• Turbulent transport and the random occurrence of coherent events
• Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation
• Chaotic and homoclinic behavior for numerical discretizations of the nonlinear Schrödinger equation
• Mel'nikov analysis of numerically induced chaos in the nonlinear Schrödinger equation
• A mean-field statistical theory for the nonlinear Schrödinger equation
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• On Homoclinic Structure and Numerically Induced Chaos for the Nonlinear Schrödinger Equation
• Nonlinear differential−difference equations
• Standing wave instabilities in a chain of nonlinear coupled oscillators

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