MiniLogo

EqWorld

The World of Mathematical Equations

IPM Logo

Exact Solutions Methods Software For Authors Math Forums

EqArchive: Add Equation/Solution > View Equation

 English only

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):$u_x=uf(au^n+bw)$,\\
$w_t=u^kg(au^n+bw)$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution with a generalized separations of variables at $n\not=k$,
$ab\not=0$:\hfill\break
$\displaystyle u=(C_1t+C_2)^{\frac 1{n-k}}\theta(x),\quad \ w=\varphi(x)-\frac
ab(C_1t+C_2)^{\frac n{n-k}}[\theta(x)]^n,$\hfill\break
where $C_1$ and $C_2$ are arbitrary constants and the functions 
$\theta=\theta(x)$ and $\varphi=\varphi(x)$ are described by the system of differential-algebraic equations:
\hfill\break
$\theta'_x=\theta f(b\varphi),\quad \
\theta^{n-k}=\cfrac{b(k-n)}{aC_1n}g(b\varphi).$
Remarks:Here $f$ and $g$ are arbitrary functions of 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 Mechanic
Statistic information
Submission date:Sat 22 Sep 2007 23:40
Edits by author:0

Edit (Only for author/contributor)


The EqWorld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations.

Copyright © 2006-2011 Andrei D. Polyanin, Alexei I. Zhurov and Alexander L. Levitin