Differential and Integral Equations

On a quasilinear Zakharov system describing laser-plasma interactions

M. Colin and T. Colin

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In this paper, starting from the bi-fluid Euler-Maxwell system, we derive a complete set of Zakharov-type equations describing laser-plasma interactions. This system involves a quasilinear part which is not hyperbolic and exhibits some elliptic zones. This difficulty is overcome by making a change of unknowns that are strongly related to the dispersive part. This change of variable is a symmetrization of the quasilinear part and is the key of this paper. This shows that the Cauchy problem is locally well-posed.

Article information

Differential Integral Equations, Volume 17, Number 3-4 (2004), 297-330.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35Q60: PDEs in connection with optics and electromagnetic theory 76X05: Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 78A60: Lasers, masers, optical bistability, nonlinear optics [See also 81V80] 82D10: Plasmas


Colin, M.; Colin, T. On a quasilinear Zakharov system describing laser-plasma interactions. Differential Integral Equations 17 (2004), no. 3-4, 297--330. https://projecteuclid.org/euclid.die/1356060435

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