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- This thesis discusses maslov ' s method , wavelet transform and their applications to asymptotic evaluation of wave equations in high frequency fields . the method of solving wave equations in caustic domain by symplectic geometrical theory , and the method of simplifying two - dimension wave equations in slowly varying nonhomogeneous medium by wavelet - transform theory are proposed . the caustics phenomena of electromagnetic wave propagation in concave reflector , the singularities of caustics , and the method of computing wave fields in and far away from the caustics in concave reflector are also discussed
本论文探讨了maslov方法在波动方程高频近似中的应用及焦散区的具体求解方法;讨论了用小波变换化简二维非均匀缓变介质条件下的波动方程;本文还讨论了凹面反射的焦散现象、凹面反射焦散区的奇性种类,讨论了二、三维凹面反射波动场非焦散区、焦散区的计算方法。