Adiabatic limit of the Zakharov-Rubenchik equation

DOI10.1016/S0034-4877(08)00006-2zbMath1141.35055MaRDI QIDQ931880

Filipe Oliveira

Publication date: 3 July 2008

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Alfvén wavesSchrödinger-like equationshyperbolic symmetric systemsZakharov-Rubenchik system

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Magnetohydrodynamics and electrohydrodynamics (76W05) First-order hyperbolic systems (35L40)

Related Items (12)

Conservative compact difference scheme for the Zakharov–Rubenchik equations ⋮ Bifurcations and exact traveling wave solutions of the Zakharov-Rubenchik equation ⋮ On the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system ⋮ A radial basis function finite difference (RBF-FD) method for numerical simulation of interaction of high and low frequency waves: Zakharov-Rubenchik equations ⋮ Arbitrarily high-order energy-preserving schemes for the Zakharov-Rubenchik equations ⋮ Radial basis function partition of unity procedure combined with the reduced-order method for solving Zakharov-Rubenchik equations ⋮ Uniform adiabatic limit of Benney type systems ⋮ Numerical methods and simulations for the dynamics of one-dimensional Zakharov-Rubenchik equations ⋮ On long-time behavior of solutions of the Zakharov–Rubenchik/Benney–Roskes system ⋮ Two numerical methods for the Zakharov-Rubenchik equations ⋮ On the Cauchy problem describing an electron-phonon interaction ⋮ Instability of the standing waves for a Benney-Roskes/Zakharov-Rubenchik system and blow-up for the Zakharov equations

Cites Work

• Unnamed Item
• The nonlinear Schrödinger limit of the Zakharov equations governing Langmuir turbulence
• Stability of the solitons for the one-dimensional Zakharov-Rubenchik equation
• On the Zakharov and Zakharov-Schulman systems
• Well-posedness for the Benney-Roskes/Zakharov-Rubenchik system
• Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
• The Complete Solution of the Long‐Wave–Short‐Wave Resonance Equations
• One-Parameter Semigroups for Linear Evolution Equations
• Well-posedness of the cauchy problem for the long wave-short wave resonance equations
• On a nonlinear Schrödinger equation arising in the theory of water waves

This page was built for publication: Adiabatic limit of the Zakharov-Rubenchik equation