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nlin.SI2021★ 5 cited
Exact solutions to homogeneous and quasi-homogeneous systems of nonlinear ODEs
Andrei D. Polyanin, Alexei I. Zhurov
This note considers fairly general quasi-homogeneous systems of first-order nonlinear ODEs and homogeneous systems of second-order nonlinear ODEs that contain arbitrary functions o…
nlin.SI2013
A new method for constructing exact solutions to nonlinear delay partial differential equations
Andrei D. Polyanin, Alexei I. Zhurov
We propose a new method for constructing exact solutions to nonlinear delay reaction--diffusion equations of the form where , , and…
nlin.SI2009
The Crocco transformation: order reduction and construction of Backlund transformations and new integrable equations
Andrei D. Polyanin, Alexei I. Zhurov
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 derivativ…