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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):$\displaystyle u_x=u^kf(u^nw^m)$,\hfill\break
$\displaystyle w_t=wg(u^nw^m)$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle u=a(t)\varphi^m(x)$,\hfill\break
$\displaystyle w=b(t)\varphi^{-n}(x)$,\hfill\break
where the functions $a(t)$, $b(t)$, and $\varphi(x)$ are determined by the
algebraic and differential equations\hfill\break
$m=a^{k-1}f(a^nb^m)$,\hfill\break
$b'_t=bg(a^nb^m)$,\hfill\break
$\varphi'_x=\varphi^{mk-m+1}$.
Novelty:New solution(s) / integral(s)
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Fri 24 Aug 2007 15:34
Edits by author:0

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