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):\noindent
$\displaystyle u_x=auw^n$,

\noindent
$\displaystyle w_t=bu^kw$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
General solution:\hfill\break
$\displaystyle u=\left(\frac {-\psi'_t(t)}{bn\psi(t)-ak\varphi(x)}\right)^{1/k},\quad \
w=\left(\frac {\varphi'_x(x)}{bn\psi(t)-ak\varphi(x)}\right)^{1/n}$,\hfill\break
where $\varphi(x)$ and $\psi(t)$ are arbitrary functions.
Novelty:Material has been fully published elsewhere
References:A.D. Polyanin, E.A. Vyazmina. New classes of exact solutions to nonlinear systems of reaction-diffusion equations. Doklady Mathematics, Vol. 74, No. 1, pp. 597-602, 2006.
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Thu 07 Dec 2006 10:45
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