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List of Equations

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

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Found 327 equations, 33 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 >>
 CategoryEquation(s)Author/
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261 4. Nonlinear Partial Differential Equations
4.6. Higher-Order Equations
\noindent
$\displaystyle \frac{\partial w}{\partial t}=a\ln w\,\frac{\partial w}{\partial x}+
wF\left(t,\,\frac 1w\frac{\partial w}{\partial x},\,\frac 1w\frac{\partial^2 w}{\partial x^2},\,\ldots,\,\frac 1w\frac{\partial^n w}{\partial x^n}\right)$. Andrei Polyanin
Submitted: 11 Dec 06 10:27
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262 4. Nonlinear Partial Differential Equations
4.6. Higher-Order Equations
\noindent
$\displaystyle \frac{\partial w}{\partial t}=
a\frac{\partial^n w}{\partial x^n}+(b\ln w+c)\frac{\partial w}{\partial x}$. Andrei Polyanin
Submitted: 10 Dec 06 13:54
Edited (admin): 11 Dec 06 11:02
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263 4. Nonlinear Partial Differential Equations
4.6. Higher-Order Equations
$\displaystyle
\dfrac{\partial w}{\partial t} + 
\dfrac{\partial ^5 w}{\partial x^5 } + 
5w\dfrac{\partial ^3 w}{\partial x^3} + 
5\dfrac{\partial w}{\partial x}\dfrac{\partial ^2 w}{\partial x^2 } + 
5 w^2\dfrac{\partial w}{\partial x} = 0.
$\newline
Sawada-Kotera equation. Alvaro Humberto Salas
Submitted: 22 May 08 19:11
Edited (admin): 16 Jun 08 09:09
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264 4. Nonlinear Partial Differential Equations
4.6. Higher-Order Equations
$\displaystyle
\frac{\partial u}{\partial t}+
\omega\frac{\partial^5u}{\partial x^5}+
\alpha u\frac{\partial^3u}{\partial x^3}+
\beta\frac{\partial u}{\partial x}\frac{\partial^2u}{\partial x^2}+
\gamma u^{2}\frac{\partial u}{\partial x}=0.$\newline
General fifth-order KdV equation. Alvaro Humberto Salas
Submitted: 19 May 08 01:04
Edited (author): 16 Jun 08 08:46
Edited (admin): 22 Jan 09 09:40
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265 4. Nonlinear Partial Differential Equations
4.7. Systems of Two Equations
\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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266 4. Nonlinear Partial Differential Equations
4.7. Systems of Two Equations
\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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267 4. Nonlinear Partial Differential Equations
4.7. Systems of Two Equations
\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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268 4. Nonlinear Partial Differential Equations
4.7. Systems of Two Equations
$\displaystyle u_x=u^kf(u^nw^m)$,\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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269 4. Nonlinear Partial Differential Equations
4.7. Systems of Two Equations
$u_t-u_{xx}=u(1-u^2-w^2)$,\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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270 4. Nonlinear Partial Differential Equations
4.7. Systems of Two Equations
$\displaystyle \begin{array}[c]{ll}
F_1\left(au^k+bw,\cfrac{u_x}{u},\cfrac{u_{xx}}{u},\dots,\cfrac{u_x^{(m)}}{u},
\cfrac{w_t}{u^k},\cfrac{w_{tt}}{u^k},\dots,\cfrac{w_t^{(n)}}{u^k}\right)&=0,\cr
F_2\left(au^k+bw,\cfrac{u_x}{u},\cfrac{u_{xx}}{u},\dots,\cfrac{u_x^{(m)}}{u},
\cfrac{w_t}{u^k},\cfrac{w_{tt}}{u^k},\dots,\cfrac{w_t^{(n)}}{u^k}\right)&=0.
\end{array}$ Elena Vyazmina
Submitted: 23 Sep 07 10:51
Edited (admin): 10 Jan 08 10:43
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Found 327 equations, 33 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 >>

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