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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):$u_x=auw^n$,\\
$w_t=bu^k$.
Solution(s),
Transformation(s),
Integral(s)
:
General Solution:\hfill\break
$\displaystyle \begin{array}[c]{ll}
w&=\varphi(x)+E(x)\left[\psi(t)-\cfrac12ak\int
E(x)\,dx\right]^{\!-1},\cr u&=\left(\cfrac 1b\cfrac{\partial w}{\partial
t}\right)^{\!1/k},\quad
E(x)=\exp\left[ak\int\varphi(x)\,dx\right],
\end{array}$\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, V. 74, No. 1, P. 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 11:20
Edits by author:0

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