Differential and Integral Equations

New distributional travelling waves for the nonlinear Klein-Gordon equation

A. Paiva and C.O.R. Sarrico

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Abstract

The present paper concerns the study of distributional travelling waves in models ruled by the nonlinear Klein-Gordon equation $u_{tt}-c^{2}u_{xx} =\phi(u)$, where $c>0$ is a real number and $\phi$ is an entire function which takes real values on the real axis. For this purpose, we use a product of distributions that extends the meaning of $\phi(u)$ to certain distributions $u$ and that allows us to define a solution concept consistent with the classical solution concept. The phi-four equation and the sine-Gordon equation are examined as particular cases.

Article information

Source
Differential Integral Equations Volume 30, Number 11/12 (2017), 853-878.

Dates
First available in Project Euclid: 1 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1504231277

Subjects
Primary: 46F10: Operations with distributions 35D99: None of the above, but in this section 35L67: Shocks and singularities [See also 58Kxx, 76L05]

Citation

Sarrico, C.O.R.; Paiva, A. New distributional travelling waves for the nonlinear Klein-Gordon equation. Differential Integral Equations 30 (2017), no. 11/12, 853--878. https://projecteuclid.org/euclid.die/1504231277


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