SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONSⅡ, NONLINEAR CAUSTIC  

作　　者：袁明生 

机构地区：[1]Department of Mathematics Shanghai Jiaotong University

出　　处：《Acta Mathematica Scientia》2007年第2期381-394,共14页数学物理学报（B辑英文版）

基　　金：The study is supported by National Natural Science Foundation of China (10131050);the Educational Ministry of China;the Shanghai Science and Technology Committee foundation (03QMH1407)

摘　　要：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.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.

关 键 词：Nonlinear wave equations spherical pulses caustic crossing nonlinearity 

分 类 号：O175.2[理学—数学]