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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):$u_x=awu$,\\
$w_t=bu^k.$
Solution(s),
Transformation(s),
Integral(s)
:
General solution:
$$\begin{array}[c]{ll}
w&=\varphi(x)+E(x)\left[\psi(t)-\cfrac{1}{2}ak\int
E(x)\,dx\right]^{-1},\cr u&=\Biggl(\cfrac{1}{b}\cfrac{\partial
w}{\partial t}\,\Biggr)^{\!1/k},\quad \
E(x)=\exp{\left[ak\int\varphi(x)\,dx\right]},\end{array}
$$
where $\varphi(x)$ and $\psi(t)$ are arbitrary functions.
Novelty:Material has been fully published elsewhere
References:A. D. Polyanin and A. V. Manzhirov. Handbook of Mathematics for Engineers and Scientists. Chapman & Hall/CRC Press, Boca Raton, 2007, p. 1337.
Author/Contributor's Details
Last name:Vyazmina
First name:Elena
Country:Russia
City:Moscow
Affiliation:Institute for Problems in Mechanics
Statistic information
Submission date:Mon 14 Jan 2008 14:02
Edits by author:0

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