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List of Equations

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

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4. Nonlinear Partial Differential Equations

4.6. Higher-Order Equations

Found 5 equations
 Equation(s)Author/
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1 \noindent
$\displaystyle \frac{\partial w}{\partial t}=a\ln w\,\frac{\partial w}{\partial x}+
wF\left(\frac 1w\frac{\partial w}{\partial x},\,\frac 1w\frac{\partial^2 w}{\partial x^2},\,\ldots,\,\frac 1w\frac{\partial^n w}{\partial x^n}\right)$. Andrei Polyanin
Submitted: 10 Dec 06 14:23
Edited (admin): 11 Dec 06 10:22
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2 \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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3 \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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4 $\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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5 $\displaystyle
\frac{\partial u}{\partial t}+
\omega\frac{\partial^5u}{\partial x^5}+
\alpha u\frac{\partial^3u}{\partial x^3}+
\beta\frac{\partial u}{\partial x}\frac{\partial^2u}{\partial x^2}+
\gamma u^{2}\frac{\partial u}{\partial x}=0.$\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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Found 5 equations

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