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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:4.7. Systems of Two Equations
Equation(s):\noindent
$\displaystyle u_x=auw^n$,\hfill\break
$\displaystyle w_t=bu^kw^{1-n}$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
General solution:
$$\displaylines{
w=\left\{\varphi(x)+E(x)\left[\psi(t)-\frac12ak\int E(x)\,dx\right]^{\!-1}\right\}^{\!1/n},\cr
u=\left(\frac 1bw^{n-1}\pd wt\right)^{\!1/k},\quad
E(x)=\exp\left[ak\int\varphi(x)\,dx\right],\cr}
$$
where $\varphi(x)$ and $\psi(t)$ are arbitrary functions.
Remarks:For $n=1$, this solution was obtained in [1].
Novelty:Material has been partially published elsewhere
References:1. Polyanin, A. D. and Vyaz'mina, E. A., New classes of exact solutions to nonlinear systems of reaction-diffusion equations, Doklady Mathematics, Vol. 74, No. 1, pp. 597--602, 2006.
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Thu 14 Dec 2006 13:32
Edits by author:0

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