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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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101 4. Nonlinear Partial Differential Equations
4.2. Second-Order Quasilinear Hyperbolic Equations
\noindent
$\displaystyle \frac{\partial^2 w}{\partial t\partial x}-
\left(\frac 1w\frac{\partial w}{\partial t}+b\right)\frac{\partial w}{\partial x}-\frac{c}{w}\frac{\partial w}{\partial t}-c b= 0$.
%where $b$ and $c$ are constants. Yurii Kosovtsov
Submitted: 11 Dec 06 08:54
Edited (author): 11 Dec 06 12:10
Edited (admin): 13 Dec 06 10:10
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102 4. Nonlinear Partial Differential Equations
4.2. Second-Order Quasilinear Hyperbolic Equations
\noindent
$\displaystyle \frac{ac}{w}+b+\frac{a}{w}\frac{\partial w}{\partial
x}-\frac{a^2}{w^4}\left(c\frac{\partial w}{\partial t}+\frac{\partial
w}{\partial t}\frac{\partial w}{\partial x}-w\frac{\partial^2
w}{\partial t\partial x}\right)^{\!2}=0$.
%where $a\neq0$, $b$, and $c$ are constants. Yurii Kosovtsov
Submitted: 11 Dec 06 11:23
Edited (admin): 13 Dec 06 10:41
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103 4. Nonlinear Partial Differential Equations
4.2. Second-Order Quasilinear Hyperbolic Equations
\noindent
$\displaystyle \frac{\partial^2 w}{\partial t\partial x}-
\left(\frac 1w\frac{\partial w}{\partial t}+b\right)\frac{\partial w}{\partial x}-\frac{c}{w}\frac{\partial w}{\partial t}-kw-cb= 0$.
%where $b\neq0$, $c$, and $k\neq0$ are constants. Yurii Kosovtsov
Submitted: 11 Dec 06 10:43
Edited (admin): 13 Dec 06 10:42
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104 4. Nonlinear Partial Differential Equations
4.2. Second-Order Quasilinear Hyperbolic Equations
\noindent
$\displaystyle \frac{\partial^2 w}{\partial t\partial x}-\frac{a}{w}\left(\frac{\partial
w}{\partial x}\right)^{\!2}-\left(\frac{1}{w}\frac{\partial w}{\partial
t}+b+\frac{c}{w}\right)\frac{\partial w}{\partial x}
-\frac{c}{2aw}\frac{\partial w}{\partial
t}-kw-\frac{bc}{2a}-\frac{c^2}{4aw} = 0$.
%where $a\neq0$, $b$, $c$, and $k$ are constants; $b^2-4ka\neq0$. Yurii Kosovtsov
Submitted: 11 Dec 06 10:54
Edited (admin): 13 Dec 06 10:44
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105 4. Nonlinear Partial Differential Equations
4.2. Second-Order Quasilinear Hyperbolic Equations
\noindent
$\displaystyle \frac{\partial^2w}{\partial t\partial x}  = \frac{1}{w}\left(\frac{\partial w}{\partial x} +a\right )\frac{\partial w}{\partial t}+bw\frac{\partial w}{\partial x}$.
%where $a$ and $b\neq 0$ are constants. Yurii Kosovtsov
Submitted: 13 Dec 06 12:17
Edited (admin): 13 Dec 06 12:27
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106 4. Nonlinear Partial Differential Equations
4.2. Second-Order Quasilinear Hyperbolic Equations
\noindent
$\displaystyle \frac{\partial^2 w}{\partial x\partial y}=f\left(\frac{\partial w}{\partial x}\right)\frac{\partial w}{\partial y}$. Andrei Polyanin
Submitted: 14 Dec 06 14:35
Edited (admin): 14 Dec 06 17:02
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107 4. Nonlinear Partial Differential Equations
4.2. Second-Order Quasilinear Hyperbolic Equations
\noindent
$\displaystyle f(w)\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}+\left[g(w)\frac{\partial w}{\partial y}-f(w)\frac{\partial w}{\partial x}\right]\frac{\partial^2 w}{\partial x\partial y}-g(w)\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2}=0$. Andrei Polyanin
Submitted: 16 Dec 06 11:44
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108 4. Nonlinear Partial Differential Equations
4.2. Second-Order Quasilinear Hyperbolic Equations
$\displaystyle \left[f(y)+\frac{\partial w}{\partial y}\right]\frac
{\partial^2 w}{\partial x\partial y}-
\left[g(x)+\frac{\partial w}{\partial x}\right]\frac
{\partial^2 w}{\partial^2 y}=0$. Valentin Feodorovich Zaitsev
Submitted: 23 Jun 07 14:32
Edited (admin): 29 Jun 07 14:19
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109 4. Nonlinear Partial Differential Equations
4.2. Second-Order Quasilinear Hyperbolic Equations
$\displaystyle \left(y\frac{\partial w}{\partial y}+aw\right)\frac{\partial^2 w}{\partial x\partial y}
-y\left[\frac{\partial w}{\partial x}+f(x)w\right]\frac{\partial^2 w}{\partial y^2}=0$,\hfill\break Valentin Feodorovich Zaitsev
Submitted: 02 Jul 07 08:33
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110 4. Nonlinear Partial Differential Equations
4.2. Second-Order Quasilinear Hyperbolic Equations
$\displaystyle \left(\frac{\partial w}{\partial y}+aw\right)\frac{\partial^2 w}{\partial x\partial y}
-\left[\frac{\partial w}{\partial x}+f(x)w\right]\frac{\partial^2 w}{\partial y^2}=0$,\hfill\break Valentin Feodorovich Zaitsev
Submitted: 02 Jul 07 08:36
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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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