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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):$u_x=f_1(x,t)u+g_1(x,t)u^{1-n}w^m$,\\
$w_t=f_2(x,t)w+g_2(x,t)u^{n}w^{1-m}$.
Solution(s),
Transformation(s),
Integral(s)
:
With the transformation $U=u^n$, $W=w^m$, the system is reduced to the following linear system:
$$\frac{\partial U}{\partial x} =nf_1(x,t)U+ng_1(x,t)W,\quad \
\frac{\partial W}{\partial t}=mf_2(x,t)W+mg_2(x,t)U.$$
Remarks:Here $f_1$, $f_2$, $g_1$, and $g_2$ are arbitrary functions of the independent variables.
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:Sun 23 Sep 2007 00:30
Edits by author:0

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