In a generalized WKB decomposition of TE waves in an inhomogeneous dielectric, the reflected component has an increasing phase inside the layer, so it is not a left-travelling nonuniform wave.
A note on the transformation of the linear differential equation into a system of the first order equations
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abstract
A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of first order equations that can be useful for analysis of the solutions of the N-th order differential equations. In particular, for the third-order linear equation the nonlinear second-order equation that plays the same role as the Riccati equation for second-order linear equation is obtained.
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Generation of a reflected wave in an inhomogeneous medium
In a generalized WKB decomposition of TE waves in an inhomogeneous dielectric, the reflected component has an increasing phase inside the layer, so it is not a left-travelling nonuniform wave.