Nonlinear Dynamics of a System of Particle-Like Wavepackets

DOI10.1007/978-0-387-75217-4_3zbMath1260.35176arXivmath/0611656OpenAlexW1479992882MaRDI QIDQ3514579

Publication date: 21 July 2008

Published in: Instability in Models Connected with Fluid Flows I (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611656

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Second-order nonlinear hyperbolic equations (35L70) Abstract hyperbolic equations (35L90) Higher-order nonlinear hyperbolic equations (35L75)

Related Items (2)

Newton's law for a trajectory of concentration of solutions to nonlinear Schrödinger equation ⋮ Wave-corpuscle mechanics for electric charges

Cites Work

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The focusing nonlinear Schrödinger equation: Effect of the coupling to a low frequency field
Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on \(\mathbb R^2\)
On soliton dynamics in nonlinear Schrödinger equations
Spectral theory and nonlinear partial differential equations: a survey
Wavepacket preservation under nonlinear evolution
Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations
Justification of modulation equations for hyperbolic systems via normal forms
Birkhoff normal form for some nonlinear PDEs
Nonlinear Maxwell equations in inhomogeneous media
Existence and stability of modulating pulse solutions in Maxwell's equations describing nonlinear optics
Polynomial normal forms with exponentially small remainder for analytic vector fields
Justification of and long-wave correction to Davey-Stewartson systems from quadratic hyperbolic systems
Long time motion of NLS solitary waves in a confining potential
Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances
Long wave approximations for water waves
Nonlinear photonic crystals: I. Quadratic nonlinearity
THE LONG WAVE LIMIT FOR A GENERAL CLASS OF 2DQUASILINEAR HYPERBOLIC PROBLEMS
LINEAR SUPERPOSITION IN NONLINEAR WAVE DYNAMICS
ASYMPTOTIC DECAY OF A ONE-DIMENSIONAL WAVE PACKET IN A NONLINEAR DISPERSIVE MEDIUM
Nonlinear photonic crystals: IV. Nonlinear Schrödinger equation regime
Nonlinear modulation of gravity waves: a rigorous approach
The validity of modulation equations for extended systems with cubic nonlinearities
Diffractive nonlinear geometric optics with rectification
Comparison of Inertial Manifolds and Application to Modulated Systems
Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems
The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities
On the validity of mean-field amplitude equations for counterpropagating wavetrains
Non-standard characteristics in asymptotic problems
Nonlinear photonic crystals: II. Interaction classification for quadratic nonlinearities
Nonlinear photonic crystals: III. Cubic nonlinearity
Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension
Normal forms for wave motion in fluid interfaces.

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