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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
$\displaystyle A(w)\left (\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial x \, \partial y}- \frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x ^2}\right)+\frac{dA(w)}{dw}}\frac{\partial w}{\partial y }\left(\frac{\partial w}{\partial x}\right)^2\\
+B(w) \left(\frac{\partial w}{\partial t}+A(w) \frac{\partial w}{\partial y}\right) \left(\frac{\partial w}{\partial x}\right)^2+\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial t \, \partial x}
 -\frac{\partial w}{\partial t}\frac{\partial^2 w}{\partial x ^2}=0$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
The general solution in implicit form ($w=w(t,x,y) $):\hfill\break
$\displaystyle x\exp \left(\int_c^wB(\zeta)\,d\zeta  \right) +\int_s^t G\left[\xi,\,y+A(w)(\xi-t)\right]\,d\xi +F[w,y-A(w)t] = 0 ,\\$\hfill\break
where $F$ and $G$ are arbitrary functions of two arguments, $c,s$ are arbitrary constants.
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:Wed 11 Jul 2007 09:46
Edits by author:0

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