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Category:4. Nonlinear Partial Differential Equations
Subcategory:4.7. Systems of Two Equations
Solution with a generalized separations of variables at $n\not=k$,
$\displaystyle u=(C_1t+C_2)^{\frac 1{n-k}}\theta(x),\quad \ w=\varphi(x)-\frac
ab(C_1t+C_2)^{\frac n{n-k}}[\theta(x)]^n,$\hfill\break
where $C_1$ and $C_2$ are arbitrary constants and the functions 
$\theta=\theta(x)$ and $\varphi=\varphi(x)$ are described by the system of differential-algebraic equations:
$\theta'_x=\theta f(b\varphi),\quad \
Remarks:Here $f$ and $g$ are arbitrary functions of a composite argument.
Novelty:Material has been fully published elsewhere
References:A.D. Polyanin and E.A. Vyaz’mina. New Classes of Exact Solutions to Nonlinear Systems of Reaction-Diffusion Equations. Doklady Mathematics, 2006, Vol. 74, No. 1, pp. 597-602.
Author/Contributor's Details
Last name:Vyazmina
First name:Elena
Affiliation:Institute for Problems in Mechanic
Statistic information
Submission date:Sat 22 Sep 2007 23:40
Edits by author:0

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