| SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONS Ⅱ, NONLINEAR CAUSTIC |
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| 引用本文： | 袁明生. SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONS Ⅱ, NONLINEAR CAUSTIC[J]. 数学物理学报(B辑英文版), 2007, 27(2): 381-394. DOI: 10.1016/S0252-9602(07)60038-1 |
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| 作者姓名： | 袁明生 |
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| 作者单位： | Department of |
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| 基金项目： | 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) |
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| 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.
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| 关 键 词： | 球形非线性脉冲 非线性波动方程 解 非线性焦散 |
| 收稿时间： | 2005-01-17 |
| 修稿时间： | 2005-05-24 |
Spherical nonlinear pulses for the solutions of nonlinear wave equations II, nonlinear caustic |
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| Mingsheng Yuan,. Spherical nonlinear pulses for the solutions of nonlinear wave equations II, nonlinear caustic[J]. Acta Mathematica Scientia, 2007, 27(2): 381-394. DOI: 10.1016/S0252-9602(07)60038-1 |
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| Authors: | Mingsheng Yuan |
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| Affiliation: | aDepartment of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China |
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| Abstract: | 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. |
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| Keywords: | Nonlinear wave equations spherical pulses caustic crossing nonlinearity |
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