On RF-pairs, Backlund transformations and linearization of nonlinear equations

作者：Polyanin A D; Zhurov A I^*

来源：Communications in Nonlinear Science & Numerical Simulation, 2012, 17(2): 536-544.

DOI：10.1016/j.cnsns.2011.03.037

• RF-pairs
• Backlund transformations
• Linearizable equations
• Order reduction of equations
• Von Mises transformation
• Exact solutions
• Navier-Stokes equations
• Boundary layer equations
• Calogero equation

Some classes of nonlinear equations of mathematical physics are described that admit order reduction through the use of a hydrodynamic-type transformation, where the unknown function is taken as a new independent variable and an appropriate partial derivative is taken as the new dependent variable. RF-pairs and associated Backlund transformations are constructed for evolution equations of general form. The results obtained are used for order reduction of hydrodynamic equations (Navier-Stokes and boundary layer) and constructing exact solutions to these equations. A generalized Calogero equation and a number of other new linearizable nonlinear differential equations of the second, third and forth orders are considered. Some integro-differential equations are analyzed.

• 出版日期2012-2