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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
$\displaystyle \frac{\partial^2w}{\partial t^2}=\frac{\partial}{\partial x}\left[f(w)\frac{\partial w}{\partial x}\right]$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Exact solutions in implicit form:
$$\displaylines{
x+t\sqrt{f(w)}=\varphi(w),\cr
x-t\sqrt{f(w)}=\psi(w),\cr}
$$
where $\varphi(w)$ and $\psi(w)$ are arbitrary functions.
Remarks:\noindent
1.\enspace This equation is encountered in wave and gas dynamics.
\medskip

\noindent
2.\enspace Probably these solutions have been already found. In this case I would be 
grateful if you send the appropriate reference to the following address:\break 
eqworld@ipmnet.ru
\medskip

\noindent
3.\enspace For other solutions, see A. D. Polyanin and V. F. Zaitsev, {\it Handbook of Nonlinear
Partial Differential Equations}, Chapman \& Hall/CRC Press,
Boca Raton, 2004 (pp.~252--255).
Novelty:New solution(s) / integral(s)
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Wed 13 Dec 2006 09:52
Edits by author:0

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