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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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251 4. Nonlinear Partial Differential Equations
4.5. Third-Order Equations
$\displaystyle \frac{\partial^2 w}{\partial x\partial y}\frac{\partial^3 w}{\partial x^2\partial y}-
\frac{\partial^2 w}{\partial y^2}\frac{\partial^3 w}{\partial x^3}+
\left[g(y)\frac{\partial^2 w}{\partial x\partial y}-f(x)\frac{\partial^2 w}{\partial y^2}\right]
\frac{\partial^2 w}{\partial x^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 14:03
Edited (admin): 10 Jan 08 14:27
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252 4. Nonlinear Partial Differential Equations
4.5. Third-Order Equations
$\displaystyle \frac{\partial w}{\partial x}\frac{\partial^3 w}{\partial x^2\partial y}-
\frac{\partial w}{\partial y}\frac{\partial^3 w}{\partial x^3}+
\left[g(y)\frac{\partial w}{\partial x}-f(x)\frac{\partial w}{\partial y}\right]
\frac{\partial^2 w}{\partial x^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 14:02
Edited (admin): 10 Jan 08 14:28
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253 4. Nonlinear Partial Differential Equations
4.5. Third-Order Equations
$\displaystyle \left(\frac{\partial^3 w}{\partial x\partial y^2}\right)^2-
\left[\frac{\partial^3 w}{\partial y^3}+
h(w)\frac{\partial w}{\partial y}+g(y)\right]\frac{\partial^3 w}{\partial x^2\partial y}+
\left[
h(w)\frac{\partial w}{\partial x}+f(x)\right]\frac{\partial^3 w}{\partial x\partial y^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 14:02
Edited (admin): 10 Jan 08 14:29
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254 4. Nonlinear Partial Differential Equations
4.5. Third-Order Equations
$\displaystyle \left[\frac{\partial^3 w}{\partial y^3}+
h(w)\frac{\partial w}{\partial y}+g(y)\right]\frac{\partial^3 w}{\partial x^3}-
\left[\frac{\partial^3 w}{\partial x\partial y^2}+
h(w)\frac{\partial w}{\partial x}+f(x)\right]\frac{\partial^3 w}{\partial x^2\partial y}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 14:01
Edited (admin): 10 Jan 08 14:30
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255 4. Nonlinear Partial Differential Equations
4.5. Third-Order Equations
$\displaystyle \left(\frac{\partial^3 w}{\partial x^2\partial y}\right)^2-
\frac{\partial^3 w}{\partial x^3}\frac{\partial^3 w}{\partial x\partial y^2}+
f\left(\frac{\partial w}{\partial y}\right)\frac{\partial^2 w}{\partial x\partial y}
\left(\frac{\partial^2 w}{\partial x\partial y}\frac{\partial^3 w}{\partial x^2\partial y}-
\frac{\partial^2 w}{\partial y^2}\frac{\partial^3 w}{\partial x^3}\right)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 14:00
Edited (admin): 10 Jan 08 14:31
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256 4. Nonlinear Partial Differential Equations
4.5. Third-Order Equations
$\displaystyle \frac{\partial^3 w}{\partial x^3}\frac{\partial^3 w}{\partial y^3}-
\frac{\partial^3 w}{\partial x^2\partial y}\frac{\partial^3 w}{\partial x\partial y^2}+
f(w)\frac{\partial^2 w}{\partial y^2}\left(\frac{\partial w}{\partial y}\frac{\partial^3 w}{\partial x^3}-
\frac{\partial w}{\partial x}\frac{\partial^3 w}{\partial x^2\partial y}\right)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:59
Edited (admin): 10 Jan 08 14:32
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257 4. Nonlinear Partial Differential Equations
4.5. Third-Order Equations
$\displaystyle \left(\frac{\partial^3 w}{\partial x^2\partial y}\right)^2-
\frac{\partial^3 w}{\partial x^3}\frac{\partial^3 w}{\partial x\partial y^2}+
f(w)\frac{\partial^2 w}{\partial x\partial y}\left(\frac{\partial w}{\partial x}\frac{\partial^3 w}{\partial x^2\partial y}-
\frac{\partial w}{\partial y}\frac{\partial^3 w}{\partial x^3}\right)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:59
Edited (admin): 10 Jan 08 14:33
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258 4. Nonlinear Partial Differential Equations
4.5. Third-Order Equations
$$ \dfrac{\partial w}{\partial t} - 
\dfrac{\partial^3 w}{\partial t \partial x^2}+
(b+1) w^2\dfrac{\partial w}{\partial x}
 = b\dfrac{\partial w}{\partial x}\dfrac{\partial^2 w}{\partial x^2}+ 
w\dfrac{\partial^3 w}{\partial x^3}.$$
Generalized modified Degasperis - Procesi equation (mDP equation). Alvaro Humberto Salas
Submitted: 19 May 08 14:07
Edited (author): 04 Jun 08 22:44
Edited (admin): 20 May 08 11:29
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259 4. Nonlinear Partial Differential Equations
4.5. Third-Order Equations
$\displaystyle \frac{\partial w}{\partial t} + 6w\frac{\partial w}{\partial x} + \frac{\partial^3 w}{\partial x^3} = 0,$\quad \
KdV equation. Alvaro Humberto Salas
Submitted: 19 May 08 14:21
Edited (admin): 20 Feb 09 15:42
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260 4. Nonlinear Partial Differential Equations
4.6. Higher-Order Equations
\noindent
$\displaystyle \frac{\partial w}{\partial t}=a\ln w\,\frac{\partial w}{\partial x}+
wF\left(\frac 1w\frac{\partial w}{\partial x},\,\frac 1w\frac{\partial^2 w}{\partial x^2},\,\ldots,\,\frac 1w\frac{\partial^n w}{\partial x^n}\right)$. Andrei Polyanin
Submitted: 10 Dec 06 14:23
Edited (admin): 11 Dec 06 10:22
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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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