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Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.7. Systems of Two Equations
Equation(s):$\displaystyle u_x=\frac{cw^nu}{a+bw^n}$,\\
$w_t=(aw+bw^{n+1})u^k$.
Solution(s),
Transformation(s),
Integral(s)
:
General solution for $b\not=0$:\hfill\break
$\displaystyle \begin{array}[c]{ll}
w&=\displaystyle \left\{\varphi(x)+E(x)\left[\psi(t)-\frac12ak\int
E(x)\,dx\right]^{\!-1}\right\}^{1/n},\cr u&=\displaystyle
\left(\frac 1bw^{n-1}\frac{\partial w}{\partial
t}\right)^{\!1/k},\quad
E(x)=\exp\left[ak\int\varphi(x)\,dx\right],
\end{array}$\hfill\break
where $\varphi(x)$ and $\psi(t)$ are arbitrary functions.
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
Country:Russia
City:Moscow
Affiliation:Institute for Problems in Mechanics
Statistic information
Submission date:Sat 22 Sep 2007 11:06
Edits by author:0

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