Derivation of the Zakharov equations
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Publication:878040
DOI10.1007/s00205-006-0034-4zbMath1370.35249arXivmath/0603092OpenAlexW1974286806MaRDI QIDQ878040
Publication date: 26 April 2007
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0603092
Pseudodifferential operators as generalizations of partial differential operators (35S05) PDEs in connection with optics and electromagnetic theory (35Q60) Singular perturbations in context of PDEs (35B25) First-order nonlinear hyperbolic equations (35L60) Turbulence (76F99) Ionized gas flow in electromagnetic fields; plasmic flow (76X05)
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Cites Work
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- Sharp estimates for pseudo-differential operators with symbols of limited smoothness and commutators
- On a quasilinear Zakharov system describing laser-plasma interactions.
- The nonlinear Schrödinger limit of the Zakharov equations governing Langmuir turbulence
- Pseudodifferential operators and nonlinear PDE
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- Existence and smoothing effect of solutions for the Zakharov equations
- On the Cauchy problem for the Zakharov system
- Transparent nonlinear geometric optics and Maxwell-Bloch equations.
- On a degenerate Zakharov system
- Kinetic theory and fluid dynamics
- Propagation of oscillations in real vanishing viscosity limit
- The short-wave limit for nonlinear, symmetric, hyperbolic systems
- THE GHOST EFFECT IN THE CONTINUUM LIMIT FOR A VAPOR–GAS MIXTURE AROUND CONDENSED PHASES: ASYMPTOTIC ANALYSIS OF THE BOLTZMANN EQUATION
- Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems
- Oscillations fortes sur un champ linéairement dégénéré
- Justification of the Zakharov Model from Klein–Gordon-Wave Systems
- Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
- Diffractive nonlinear geometric optics with rectification