Particular solutions of equations with multiple characteristics expressed through hypergeometric functions

Abstract In the paper, similarity solutions are constructed for a model equation with multiple characteristics of an arbitrary integer order. It is shown that the structure of similarity solutions depends on the mutual simplicity of the orders of derivatives with respect to the variable x and y , respectively. Frequent cases are considered in which they are shown as fundamental solutions of well-known equations, expressed in a linear way through the constructed similarity solutions.

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