Von Mises- and Crocco-type hydrodynamical transformations: order reduction of nonlinear equations, construction of Bäcklund transformations and of new integrable equations
type: Item
instance of: scholarly article
title: Von Mises- and Crocco-type hydrodynamical transformations: order reduction of nonlinear equations, construction of Bäcklund transformations and of new integrable equations
zbMATH Open document ID: 1268.35105
DOI: 10.1134/S1061920811030034
author: A. D. Polyanin
author: I. A. Fedotov
published in: Russian Journal of Mathematical Physics
publication date: 2012-10-22T00:00:00Z
review text: The von Mises transformation is a transformation in which the unknown function is used as a new independent variable and a partial derivative with respect to the coordinate directed along the normal to the streamlined surface is the new dependent variable. The Crocco transformation is a transformation in which the first and second derivatives are used as new independent and dependent variables, respectively. These transformations, which are used in hydrodynamics in the study of boundary layer equations, are employed in this paper to reduce the order of a broad class of nonlinear equations with mixed derivatives. Several examples of nonlinear equations admitting a reduction of order by using these two types of transformations are presented. Also, by using von Mises and Crocco transformations in a wide class of evolution equations, the authors construct Bäcklund transformations and use them to construct new integrable equations. Some examples of equations with three independent variables are also considered.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 76D10
zbMATH DE Number: 6097090
MaRDI profile type: Publication
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full work available at URL: s1061920811030034
OpenAlex ID: W2058875007
description: scientific article; zbMATH DE number 6097090