Publisher： John Wiley & Sons Inc
E-ISSN： 1467-9590|88|3|173-190
ISSN： 0022-2526
Source： STUDIES IN APPLIED MATHEMATICS, Vol.88, Iss.3, 1993-04, pp. : 173-190
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
This paper shows how to use the method of quasisolutions to construct exact solutions to Burgers’ equation. A function υ=υ(x, y) is called a quasisolution of a PDE in case there exists a function φ (not a constant function) of one variable so that u(x, y)=φ(υ(x, y)) is a solution of the equation. We prove a theorem giving necessary and sufficient conditions for υ to be a quasisolution to Burgers’ equation. A function φ can then be found explicitly so that u=φ(υ) is an actual solution. Combining this technique with similarity methods, we find a continuum of solutions to Burgers' equation.
Related content
Some Closed‐Form Solutions of Burgers’ Equation
STUDIES IN APPLIED MATHEMATICS, Vol. 88, Iss. 3, 1993-04 ,pp. :
Access to resources
Recommend
Exact Closed-Form Solutions of Some Nonlinear Differential Equations
Differential Equations, Vol. 40, Iss. 8, 2004-08 ,pp. :
New explicit solutions of the Burgers equation
By Qin Maochang Mei Fengxiang Fan Guihong
Nonlinear Dynamics, Vol. 48, Iss. 1-2, 2007-04 ,pp. :