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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):$u_x=uf(au^k+bw)$,\\
$w_t=cu^k$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle w=\varphi(x)+C\exp\left[-\lambda t+k\int
f(b\varphi(x))\,dx\right],\quad \
u=\left(\frac{1}{c}\frac{\partial w}{\partial
t}\right)^{1/k},\quad \ \lambda=\frac {bc}{a},$\hfill\break
where $\varphi(x)$ is an arbitrary function, $C$ is an arbitrary constant.
Remarks:Here $f$ is an arbitrary function depending on 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
Country:Russia
City:Moscow
Affiliation:Institute for Problems in Mechanics
Statistic information
Submission date:Sat 22 Sep 2007 23:31
Edits by author:0

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