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View Equation

The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.1. Second-Order Quasilinear Parabolic Equations
Equation(s):\noindent
$\displaystyle \frac{\partial w}{\partial t}=a\frac{\partial^2 w}{\partial x^2}-bw^2.$
Solution(s),
Transformation(s),
Integral(s)
:
\noindent 1. Exact solution:\hfill\break
$\displaystyle w=\frac ab\frac{12(4-\sqrt 6\,)x^2+12(4-\sqrt 6\,)C_1x+120(12-5\sqrt 6\,)at+12(2-\sqrt 6\,)C_2+6C_1^2}
{[x^2+C_1x+10(3-\sqrt 6\,)at+C_2]^2},$\hfill\break
where $C_1$ and $C_2$ are arbitrary constants.
\medskip

\noindent 2. Exact solution:\hfill\break
$\displaystyle w=\frac ab\frac{12(4+\sqrt 6\,)x^2+12(4+\sqrt 6\,)C_1x+120(12+5\sqrt 6\,)at+12(2+\sqrt 6\,)C_2+6C_1^2}
{[x^2+C_1x+10(3+\sqrt 6\,)at+C_2]^2}},$\hfill\break
where $C_1$ and $C_2$ are arbitrary constants.
Novelty:Material has been partially published elsewhere
References:Barannyk T. A. Symmetry and exact solutions for systems of nonlinear reaction-diffusion equations. Proc. of Inst. of Mathematics of NAS of Ukraine, Vol. 43, Part 1, pp. 80--85, 2002.
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Wed 06 Dec 2006 11:22
Edits by author:1
Last edit by author:Mon 11 Dec 2006 11:39

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