Integrability revisited: a necessary condition

DOI10.1016/S0375-9601(01)00384-XzbMath0969.37526MaRDI QIDQ5937761

Panayotis G. Kevrekidis

Publication date: 15 July 2001

Published in: Physics Letters. A (Search for Journal in Brave)

zbMATH Keywords

internal soliton modes

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

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The complete solution of the Schrödinger equation with the Rosen-Morse type potential via the Nikiforov-Uvarov method ⋮ On a class of discretizations of Hamiltonian nonlinear partial differential equations ⋮ Resonant interaction of \(\phi^4\) kink with \(\mathcal{PT}\)-symmetric perturbation with spatially periodic gain/loss coefficient ⋮ Transient radiative behavior of Hamiltonian systems in finite domains ⋮ The asymptotic stability of solitons in the cubic NLS equation on the line ⋮ Planar Skyrmions: vibrational modes and dynamics ⋮ Decay of bound states in a sine-Gordon equation with double-well potentials ⋮ The parametrically modified sine-Gordon equation: Spectral properties, collisions, resonances and their connection to integrability ⋮ Stability of solitary waves in nonlinear Klein–Gordon equations

Cites Work

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• Stability of waves in discrete systems
• Edge Bifurcations for Near Integrable Systems via Evans Function Techniques
• A discrete $\phi^4$ system without a Peierls - Nabarro barrier
• The inverse scattering transform: Semi-infinite interval
• Nonlinear differential–difference equations and Fourier analysis

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