Andrei D. Polyanin, Alexei I. Zhurov. The Crocco transformation: order reduction and construction of Backlund transformations and new integrable equations
Natural Sciences / Physics / Mathematical Physics
Submitted on: Jul 15, 2012, 07:07:01
Description: 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.