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List of Equations

The database contains 327 equations (8 equations are awaiting activation).

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See also: Categorized List of Equations

4. Nonlinear Partial Differential Equations

4.7. Systems of Two Equations

Found 27 equations, 3 pages (10 eqs. per page): << 1 2 3 >>
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1 \noindent
$u_t=[f(t,bu-cw)u_x]_x+g(t,bu-cw)$,\hfill\break
$w_t=[f(t,bu-cw)w_x]_x+h(t,bu-cw)$. Andrei Polyanin
Submitted: 06 Dec 06 13:45
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2 \noindent
$\displaystyle u_x=auw^n$,

\noindent
$\displaystyle w_t=bu^kw$. Andrei Polyanin
Submitted: 07 Dec 06 10:45
Edited (admin): 13 Dec 06 11:50
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3 \noindent
$\displaystyle u_x=auw^n$,\hfill\break
$\displaystyle w_t=bu^kw^{1-n}$. Andrei Polyanin
Submitted: 14 Dec 06 13:32
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4 $\displaystyle u_x=u^kf(u^nw^m)$,\hfill\break
$\displaystyle w_t=wg(u^nw^m)$. Andrei Polyanin
Submitted: 24 Aug 07 15:34
Edited (admin): 22 Sep 07 09:08
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5 $u_t-u_{xx}=u(1-u^2-w^2)$,\hfill\break\quad 
$w_t-w_{xx}=-2u^2w$. Konstantin Alexandrovich Volosov
Submitted: 22 Sep 07 09:04
Edited (admin): 22 Sep 07 09:09
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6 $\displaystyle \begin{array}[c]{ll}
F_1\left(au^k+bw,\cfrac{u_x}{u},\cfrac{u_{xx}}{u},\dots,\cfrac{u_x^{(m)}}{u},
\cfrac{w_t}{u^k},\cfrac{w_{tt}}{u^k},\dots,\cfrac{w_t^{(n)}}{u^k}\right)&=0,\cr
F_2\left(au^k+bw,\cfrac{u_x}{u},\cfrac{u_{xx}}{u},\dots,\cfrac{u_x^{(m)}}{u},
\cfrac{w_t}{u^k},\cfrac{w_{tt}}{u^k},\dots,\cfrac{w_t^{(n)}}{u^k}\right)&=0.
\end{array}$ Elena Vyazmina
Submitted: 23 Sep 07 10:51
Edited (admin): 10 Jan 08 10:43
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7 $u_t=ax^{-n}(x^nu_x)_x+uf_1(w/u)+wg_1(w/u)$,\\
$w_t=ax^{-n}(x^nw_x)_x+uf_2(w/u)+wg_2(w/u)$. Elena Vyazmina
Submitted: 25 Jan 08 12:24
Edited (admin): 28 Jan 08 11:33
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8 $u_t=[f(w/u)u_x]_x+ug_1(w/u)+wh_1(w/u)$, \\
$w_t=[f(w/u)w_x]_x+ug_2(w/u)+wh_2(w/u)$. Elena Vyazmina
Submitted: 25 Jan 08 12:25
Edited (admin): 28 Jan 08 11:37
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9 $$
\begin{array}[c]{ll} \vspace{0.1cm}
F_1\left(w,\cfrac{\partial w}{\partial x},\dots,\cfrac{\partial^m
w}{\partial x^m},\cfrac{1}{u^k}\,\cfrac{\partial w}{\partial t}
,\cfrac 1u\,\cfrac{\partial u}{\partial x} ,\dots,\cfrac
1u\,\cfrac{\partial^n w}{\partial x^n}\right)=0,\cr
F_2\left(w,\cfrac{\partial w}{\partial x},\dots,\cfrac{\partial^m
w}{\partial x^m},\cfrac{1}{u^k}\,\cfrac{\partial w}{\partial
t},\cfrac 1u\,\cfrac{\partial u}{\partial x},\dots,\cfrac
1u\,\cfrac{\partial^n u}{\partial x^n}\right)=0.
\end{array}
$$ Elena Vyazmina
Submitted: 25 Jan 08 12:26
Edited (admin): 28 Jan 08 11:40
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10 $u_x=auw^n$,\\
$w_t=bu^k$. Elena Vyazmina
Submitted: 22 Sep 07 11:20
Edited (admin): 29 Jan 08 15:32
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Found 27 equations, 3 pages (10 eqs. per page): << 1 2 3 >>

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