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In this paper, the scattering behaviour of an electromagnetic wave by vortex flow is studied in detail by solving the first-order (in v/c) Maxwell's equation in the cylindrical coordinate system (r, φ, z) and the general solutions are obtained. From these solutions, the differential cross-section of the vortex flow is calculated and the electromagnetic scattering characteristics of the vortex flow...
We study finite time singularities of solutions of the single phase Whitham equations for the KdV equation. We show that the first derivative of the Whitham solution blows up in a finite time for certain initial data. The key element in our analysis is the Riccati equations that govern the evolution of the first spatial derivatives of the Whitham solution along the characteristics.
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