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

DOI10.1016/j.cnsns.2011.03.037zbMath1245.35086OpenAlexW1991861927MaRDI QIDQ430313

Alexei I. Zhurov, Andrei D. Polyanin

Publication date: 21 June 2012

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2011.03.037

zbMATH Keywords

Navier-Stokes equationsexact solutionsBäcklund transformationsboundary layer equationsCalogero equationlinearizable equationsorder reduction of equationsRF-pairsvon Mises transformation

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Integro-partial differential equations (35R09)

Related Items

Parametrically defined nonlinear differential equations, differential-algebraic equations, and implicit ODEs: transformations, general solutions, and integration methods ⋮ Direct functional separation of variables and new exact solutions to axisymmetric unsteady boundary-layer equations ⋮ A primer on eigenvalue problems of non-self-adjoint operators ⋮ The fifth-order partial differential equation for the description of the \(\alpha+\beta\) Fermi-Pasta-Ulam model

Uses Software

• Maple
• Matlab
• ATFM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A transformed rational function method and exact solutions to the \(3+1\) dimensional Jimbo-Miwa equation
• Bäcklund transformation, nonlinear superposition formula and solutions of the Calogero equation
• An auto-Bäcklund transformation and exact solutions to a generalized KdV equation with variable coefficients and their applications
• Exp-function method for nonlinear wave equations
• A note on new exact solutions for the Kawahara equation using Exp-function method
• Exact solutions of unsteady three-dimensional Navier-Stokes equations
• Bäcklund transformations and their applications
• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
• Nonclassical symmetries and Bäcklund transformations
• The Calogero equation and Liouville-type equations
• On Bäcklund transformation for a generalized Burgers equation and solitonic solutions
• A multiple exp-function method for nonlinear differential equations and its application
• Reciprocal auto-Backlund transformations
• A Solvable Nonlinear Wave Equation
• Hodograph Transformations of Linearizable Partial Differential Equations
• On the remarkable nonlinear diffusion equation (∂/∂x)[a (u+b)−2(∂u/∂x)−(∂u/∂t)=0]
• Bäcklund transformations for nonlinear parabolic equations: the general results
• The tanh method: I. Exact solutions of nonlinear evolution and wave equations
• Bäcklund transformation and the Painlevé property
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I