Short-wave Equations Research Articles

On a certain class of exact particular solutions of the short-wave equations: PMM vol. 34, n≗6, 1970, pp. 1150–1158

A class of exact particular of the short-wave equations is investigated; the class in question generalizes the familiar solutions in [1,2]. The solutions are classified. Examples of new solutions are cited. Flows with small but abrupt changes in the flow parameters occuring in a narrow zone near the front of a propagating shock wave are described by the systems of short-wave equations derived in [3]. The system of short waves, which constitutes a nonlinear system of equations of mixed type, is in certain sense similar to the system of equations for steady transonic gas motions; unlike the latter system, however, it cannot be transformed into a system of linear equations. This fact complicates the mathematical statement and solution of the short-wave equations considerably, making it necessary to construct exact particular solutions with certain properties associated with a given class of physical problems. Such solutions have been obtained in various artificial ways in each specific case [2–5]. The most general of the known solutions is the class of exact solutions derived in [1]. An example of a solution not belonging to the class obtained in [1] is constructed in [2].