Highly localized solutions of the wave equation (Q2737910)
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scientific article; zbMATH DE number 1639100
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Highly localized solutions of the wave equation |
scientific article; zbMATH DE number 1639100 |
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Highly localized solutions of the wave equation (English)
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30 August 2001
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global estimates
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wave packets exponentially localized near a point
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large-time asymptotics
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Simple explicit solutions of the linear wave equation in three dimensions are presented which describe wave packets exponentially localized near a point moving with the wave speed. For large values of a certain free parameter these new solutions are localized in Gaussian manner with respect to longitudinal and transverse variables and time. This agrees with considerations by Babich-Ulin and Ralston who have presented an asymptotic description of solutions exhibiting such local behavior. Global estimates and large-time asymptotics of these solutions are given.
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