Abstract
Non-reflective wave propagation is of great importance for applications because it allows energy to be transmitted over long distances. The paper discusses the method of reducing the equations of the linear theory of shallow water to a wave equation with a variable coefficient in the form of an inverse hyperbolic sine, the solution of which is represented as a composition of traveling waves. Thanks to this, a new non-reflective bottom profile has been obtained, which reaches a constant at infinity. Wave behavior on the shore is discussed, as well as the conditions under which the wave field remains finite on it. A detailed analysis of the obtained exact solution to the shallow water equations is given in the paper.
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