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View Equation

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

Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.2. Second-Order Quasilinear Hyperbolic Equations
Equation(s):\noindent
$\displaystyle \left(\frac{\partial w}{\partial y}\right )^2\frac{\partial^2 w}{\partial t \, \partial x} -\left(\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial t \, \partial y}   +\frac{\partial w}{\partial t}\frac{\partial^2 w}{\partial x \, \partial y}\right ) \frac{\partial w}{\partial y}+\frac{\partial w}{\partial t}\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2} = a\left(\frac{\partial w}{\partial y}\right )^3 $
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
General solution in implicit form ($w=w(t,x,y)$):\hfill\break
$\displaystyle   F\left[t,G(x,w)\,\exp\left( \frac{a(t+cx)^2}{2c}+y\right )\right ]=0$,\hfill\break
where $F$, $G$ are arbitrary functions of two arguments and $c$ is an arbitrary constant.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Kosovtsov
First name:Yurii
Country:Ukraine
City:Lvov
Statistic information
Submission date:Fri 03 Aug 2007 09:25
Edits by author:0

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