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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
$u_t=[f(t,bu-cw)u_x]_x+g(t,bu-cw)$,\hfill\break
$w_t=[f(t,bu-cw)w_x]_x+h(t,bu-cw)$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Solution:\hfill\break
$\displaystyle u=\varphi(t)+c\theta(x,\tau),\quad w=\psi(t)+b\theta(x,\tau),\quad \tau=\int f(t,b\varphi-c\psi)\,dt$,\hfill\break
where the functions $\varphi=\varphi(t)$ and $\psi=\psi(t)$
are determined by the system of ordinary differential equations\hfill\break
$\varphi'_t=g(t,b\varphi-c\psi),\quad \ \psi'_t=h(t,b\varphi-c\psi)$,\hfill\break
and the function $\theta=\theta(x,\tau)$ satisfies the linear heat equation\hfill\break
$\theta_\tau=\theta_{xx}$.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Wed 06 Dec 2006 13:45
Edits by author:0

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