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 ...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.展开更多
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.
文摘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.
