Differential and Integral Equations

Fully nonlinear gauge invariant evolution of the plane wave

Kazuyuki Doi

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We consider fully nonlinear gauge invariant evolution of the plane wave. Although the plane wave does not decay at infinity, by an elementary and simple argument we find an extremely smooth solution which has an explicit expression. Additionally, we study the global behavior of the solution from its representation.

Article information

Differential Integral Equations, Volume 21, Number 9-10 (2008), 851-858.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35G25: Initial value problems for nonlinear higher-order equations
Secondary: 35B40: Asymptotic behavior of solutions 35B44: Blow-up 35C05: Solutions in closed form 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]


Doi, Kazuyuki. Fully nonlinear gauge invariant evolution of the plane wave. Differential Integral Equations 21 (2008), no. 9-10, 851--858. https://projecteuclid.org/euclid.die/1356038589

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