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Focusing of Spherical Nonlinear Pulses for Nonlinear Wave Equations 被引量：2

Focusing of Spherical Nonlinear Pulses for Nonlinear Wave Equations
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摘要 This paper describes the behavior of spherical pulse solutions of a system of semilinear wave equations in three space variables. Away fi＇om the focal point, we describe solutions with nonlinear geometric optics. We show that the approximation given by nonlinear geometric optics is valid before and after the focal point. We obtain a global asymptotic description including an approximation which is a solution of the linear wave equations near the caustic. This paper describes the behavior of spherical pulse solutions of a system of semilinear wave equations in three space variables. Away fi＇om the focal point, we describe solutions with nonlinear geometric optics. We show that the approximation given by nonlinear geometric optics is valid before and after the focal point. We obtain a global asymptotic description including an approximation which is a solution of the linear wave equations near the caustic.
作者 Ming-sheng Yuan
机构地区 Department of Mathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2005年第3期415-428,共14页 应用数学学报（英文版）
基金 Supported by the National Natural Science Foundation of China （No.10131050）, the Educational Ministry of China and the Shanghai Science and Technology Committee grant 03QMH1407.
关键词 Nonlinear wave equations spherical pulses FOCUSING Nonlinear wave equations, spherical pulses, focusing
分类号 O435 [机械工程—光学工程]
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参考文献12

  • 1Alterman, D., Rauch, J. Nonlinear geometric optics for short pulses. J. Diff. Eq., 178(2): 437-465 (2002).
  • 2Alterman, D.I Rauch, J. Diffractive nonlinear geometric optics for short pulses. SIAM J. Math. Anal., 34:1477-1502 (2003).
  • 3Alterman, D., Rauch, J. Diffractive Short Pulse Asymptotics for Nonlinear Wave Equations. Phys. Lett.A, 264(5): 390-395 (2000).
  • 4Carles,R., Rauch, J. Focusing of spherical nonlinear pulses in R^1+3 . Proc. Amer. Math. Soc., 130(3):791-804 (2002) (electronic).
  • 5Carles, R., Rauch, J. Focusing of spherical nonlinear pulses in R^1+3, Ⅱ. Nonlinear caustic. Rev. Mat.Ibcroamericana, 20:815-864 (2004).
  • 6Carles, R., Rauch, J. Absorption d'imopulsions non lindaires radiales focalisantes dans R^1+:3 C.R. Acad.Sci. Paris, Sdr. I Math.. 332(11): 985-990 (2001).
  • 7Carles, RI, Rauch, J. Diffusion d'impulsions non lineaires radiales docalisantes dans R^1+:3. C.R. Acad.Sci. Paris, Sdr. I Math., 332(12): 1077-1082 (2001).
  • 8Gerard, P. Oscillations and concentration effects in semilinear dispersive wave equations, J. Funct. Anal.,141:60-98 (1996).
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  • 10Joly, J.L., M6tivier, G., Rauch, J. Focusing at a point and absorptioon of nonlinear oscillations. Tran.Amer. Math. Sco., 347(10): 3921-3969 (1995).

同被引文献23

  • 1袁明生.一维非线性脉冲波的两波干扰[J].西安理工大学学报,2005,21(3):261-267. 被引量：2
  • 2袁明生.SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONSⅡ, NONLINEAR CAUSTIC[J].Acta Mathematica Scientia,2007,27(2):381-394. 被引量：1
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  • 6Majda A,Rosales R.A theory for spontaneous Mach-stem formation in reacting shock fronts.Ⅱ.Steady-wave bifurcations and the evidence for breakdown[J].Stud Appl Math,1984,71(2):117-148.
  • 7Majda A,Rosales R.Nonlinear mean field-high frequency wave interactions in the induction zone[J].SIAM J Appl Math,1987,47 (5):1017-1039.
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  • 10Hunter J K,Keller J B.Erratum:Weak shock diffraction[J].Wave Motion,1984,6 (1):79-89.

引证文献2

Acta Mathematicae Applicatae Sinica
2005年 第3期

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