On a class of discretizations of Hamiltonian nonlinear partial differential equations

DOI10.1016/S0167-2789(03)00153-2zbMath1031.70001MaRDI QIDQ1401532

Panayotis G. Kevrekidis

Publication date: 17 August 2003

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

zbMATH Keywords

nonlinear Schrödinger equationKlein-Gordon equationstatic solutionsHamiltonian systempartial differential equationsnonintegrabilityPeierls-Nabarro barrierdifferential-difference equationstranslational invarianceintegral-of-motion preservationmomentum integral of motion

Mathematics Subject Classification ID

Related Items (22)

Collision of \(\phi^4\) kinks free of the Peierls-Nabarro barrier in the regime of strong discreteness ⋮ Domain wall and periodic solutions of coupled ϕ4 models in an external field ⋮ On a class of spatial discretizations of equations of the nonlinear Schrödinger type ⋮ Asymptotic calculation of discrete non-linear wave interactions ⋮ Dynamical transitions between equilibria in a dissipative Klein-Gordon lattice ⋮ Translationally invariant kink solutions of discrete \(\varphi^4\) models ⋮ Necessary conditions for breathers on continuous media to approximate breathers on discrete lattices ⋮ Effect of damping on kink ratchets in the Klein-Gordon lattice free of the Peierls-Nabarro potential ⋮ Traveling monotonic fronts in the discrete Nagumo equation ⋮ Studying Davydov's ODE model of wave motion in \(\alpha \)-helix protein using exactly energy-momentum conserving discretizations for Hamiltonian systems ⋮ Nonautonomous discrete rogue wave solutions and interactions in an inhomogeneous lattice with varying coefficients ⋮ Moving embedded lattice solitons ⋮ Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: application to the vibrating piano string ⋮ Normal form for travelling kinks in discrete Klein-Gordon lattices ⋮ Bifurcations of travelling wave solutions in the discrete NLS equations ⋮ Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices ⋮ Approximate controllability of nonlinear stochastic partial differential systems with infinite delay ⋮ Discrete nonlinear Schrödinger equations free of the Peierls-Nabarro potential ⋮ Propagation failure in the discrete Nagumo equation ⋮ Exceptional Discretizations of the NLS: Exact Solutions and Conservation Laws ⋮ Stationary multi-kinks in the discrete sine-Gordon equation ⋮ Non-holonomic constraints and their impact on discretizations of Klein-Gordon lattice dynamical models

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