Abstract
Approximate travelling wave solutions to linear, one-dimensional wave equations with varying coefficients (the case of an inhomogeneous medium) are usually found using asymptotic procedures such as the WKB approach. For certain conditions put on the coefficients, this procedure leads to exact solutions . We show that such exact travelling wave solutions exist for a limited class of strongly inhomogeneous media and prove the existence and uniqueness of such waves. Using the obtained solutions, the solution of the relevant Cauchy problem is expressed in elementary functions. This approach enables a detailed and straightforward analysis of the processes of wave transformation and reflection in a specific type of strongly inhomogeneous media.
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