SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONS Ⅱ, NONLINEAR CAUSTIC

This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operat...

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Bibliographic Details
Published in:Acta Mathematica Scientia 2007-04, Vol.27 (2), p.381-394
Main Author: 袁明生
Format: Article
Language:English
Subjects:
球形非线性脉冲
非线性波动方程
非线性焦散
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Summary:This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L^∞ norms, it analyzes the relative errors in approximate solutions.
ISSN:0252-9602
1572-9087
1003-3998
DOI:10.1016/S0252-9602(07)60038-1