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arXiv · 0907.3170

The Crocco transformation: order reduction and construction of Backlund transformations and new integrable equations

Andrei D. Polyanin·Alexei I. Zhurov
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Abstract

Wide classes of nonlinear mathematical physics equations are described that admit order reduction through the use of the Crocco transformation, with a first-order partial derivative taken as a new independent variable and a second-order partial derivative taken as the new dependent variable. Associated Backlund transformations are constructed for evolution equations of general form (special cases of which are Burgers, Korteweg-de Vries, and many other nonlinear equations of mathematical physics). The results obtained are used for order reduction and constructing exact solutions of hydrodynamics equations (Navier-Stokes, Euler, and boundary layer). A number of new integrable nonlinear equations, inclusive of the generalized Calogero equation, are considered.

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BibTeXRIS

Andrei D. Polyanin, Alexei I. Zhurov. 2009-10-08. The Crocco transformation: order reduction and construction of Backlund transformations and new integrable equations. https://arxiv.org/abs/0907.3170

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