In this paper we study the propagation of weakly nonlinear surface waves on a
plasma-vacuum interface. In the plasma region we consider the equations of
incompressible magnetohydrodynamics, while in vacuum the magnetic and electric
fields are governed by the Maxwell equations. A surface wave propagate along
the plasma-vacuum interface, when it is linearly weakly stable.
  Following the approach of Ali and Hunter, we measure the amplitude of the
surface wave by the normalized displacement of the interface in a reference
frame moving with the linearized phase velocity of the wave, and obtain that it
satisfies an asymptotic nonlocal, Hamiltonian evolution equation. We show the
local-in-time existence of smooth solutions to the Cauchy problem for the
amplitude equation in noncanonical variables, and we derive a blow up
criterion.Comment: arXiv admin note: text overlap with arXiv:1305.5327 by other author

A Marcou

G Alì

JK Hunter

MF Hamilton

N Mandrik

S Benzoni-Gavage

English

arXiv

In this paper we present a recent result about the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields are governed by the Maxwell equations. A surface wave propagate along the plasma-vacuum interface, when it is linearly weakly stable.
Following the approach of Alì and Hunter, we measure the amplitude of the surface wave by the normalized displacement of the interface in a reference frame moving with the linearized phase velocity of the wave, and obtain that it satisfies an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. We show the local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables, and we derive the regularity of the first order corrections of the asymptotic expansion

SECCHI, Paolo

Archivio istituzionale della ricerca - Università di Brescia

On the amplitude equation of approximate surfacewaves on the plasma-vacuum interface

In this paper we study the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields are governed by the Maxwell equations. A surface wave propagates along the plasma-vacuum interface when it is linearly weakly stable. Following the approach of Ali and Hunter (2003), we measure the amplitude of the surface wave by the normalized displacement of the interface in a reference frame moving with the linearized phase velocity of the wave, and obtain that it satisfies an asymptotic nonlocal, Hamiltonian evolution equation. We show the local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables, and we derive a blow up criterion