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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

4.2. Second-Order Quasilinear Hyperbolic Equations

Found 41 equations, 5 pages (10 eqs. per page): << 1 2 3 4 5 >>
 Equation(s)Author/
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31 $\displaystyle \frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}-
\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial x\partial y}-
f(y)\frac{\partial w}{\partial x}=0$. Valentin Zaitsev
Submitted: 22 Aug 07 17:38
Edited (admin): 23 Aug 07 10:05
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32 $\displaystyle \frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}-
\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial x\partial y}-
[f(x)+g(y)]\left(\frac{\partial w}{\partial x}\right)^2+
f'(x)y\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}=0$. Valentin Zaitsev
Submitted: 22 Aug 07 17:41
Edited (admin): 24 Aug 07 15:26
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33 $\displaystyle \frac{\partial^2 w}{\partial x^2}+
\left[\frac{\partial w}{\partial x}-f(x)y\right]\frac{\partial^2 w}{\partial x\partial y}-
f(x)y\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2}=0$. Valentin Zaitsev
Submitted: 04 Sep 07 17:47
Edited (admin): 06 Sep 07 11:10
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34 \noindent
$\displaystyle \left[(a_2b_1-a_1b_2)w-a_1b_3+b_1a_3\right]\frac{\partial^2 w}{\partial t\partial x} &=
\left[(a_2b_1-a_1b_2)\frac{\partial w}{\partial t}+
a_2b_3-a_3b_2\right]\,\frac{\partial w}{\partial x}\notag \\\notag \\
&-(b_1\frac{\partial w}{\partial t}+b_2w+b_3)^2\,F \left(\frac{a_1\frac{\partial w}{\partial t}+a_2w+a_3}{b_1\frac{\partial w}{\partial t}+b_2w+b_3}\right)$. Yurii Kosovtsov
Submitted: 08 Dec 06 09:02
Edited (author): 20 Dec 06 11:02
Edited (admin): 11 Jan 08 09:39
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35 \noindent
$\displaystyle \left(\frac{\partial
w}{\partial x}\right)^2\frac{\partial^2 w}{\partial
t^2}-\left(\frac{\partial w}{\partial t}\right)^2\frac{\partial^2
w}{\partial x^2}=0$.
%where $c$ and $k$ are constants. Yurii Kosovtsov
Submitted: 08 Feb 08 13:10
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36 \noindent
$\displaystyle \left(w\frac{\partial^2 w}{\partial x  \partial
y}+\frac{\partial w}{\partial x}\frac{\partial w}{\partial
y}\right)^2=\left[w\frac{\partial^2 w}{\partial
x^2}+\left(\frac{\partial w}{\partial
x}\right)^2-1\right]\left[w\frac{\partial^2 w}{\partial
y^2}+\left(\frac{\partial w}{\partial y}\right)^2-1\right]\,$. Yurii Kosovtsov
Submitted: 13 Feb 08 11:01
Edited (admin): 13 Feb 08 16:36
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37 \noindent
$\displaystyle \Phi\left(t,\,\frac{\frac{\partial^2 w}{\partial t  \partial
x}}{\frac{\partial w}{\partial x}}-2bw,\,w\,\frac{\frac{\partial^2
w}{\partial t  \partial x}}{\frac{\partial w}{\partial
x}}-\frac{\partial w}{\partial t}-bw^2\right)=0$. Yurii Kosovtsov
Submitted: 25 Feb 08 10:57
Edited (admin): 06 Mar 08 12:51
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38 \noindent
$\ \displaystyle \frac{\partial^2 w}{\partial
t^2}\,\frac{\partial^2 w}{\partial x^2}-\left(\frac{\partial^2
w}{\partial t\partial x}\right)^2+\frac{\partial^2 w}{\partial
t\partial y}+\frac{\partial^2 w}{\partial x\partial z}=0$.
\vskip 0.2cm
\emph{Plebanski
second Heavenly equation.} Yurii Kosovtsov
Submitted: 25 Jun 08 10:07
Edited (author): 30 Jun 08 09:39
Edited (admin): 25 Jun 08 11:56
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39 \noindent
$\ \displaystyle \frac{\partial^2 w}{\partial
t\partial z}\,\frac{\partial^2 w}{\partial x\partial
y}-\frac{\partial^2 w}{\partial t\partial x}\,\frac{\partial^2
w}{\partial y\partial z}-1=0.$
\vskip 0.2cm
\emph{Plebanski
first Heavenly equation.} (See References [1]) Yurii Kosovtsov
Submitted: 18 Apr 08 10:18
Edited (author): 09 Jul 08 12:17
Edited (admin): 21 Apr 08 08:50
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40 \noindent
$\displaystyle \frac{\partial^2 w}{\partial t \, \partial x}  = w \frac{\partial^2 w}{\partial t^2 }$ Yurii Kosovtsov
Submitted: 16 Jul 07 10:00
Edited (author): 03 Feb 09 11:05
Edited (admin): 20 Jul 07 09:38
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Found 41 equations, 5 pages (10 eqs. per page): << 1 2 3 4 5 >>

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