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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
$\displaystyle \frac{\partial^2w}{\partial t^2}=
\frac{\partial}{\partial x}\left[f(w)\frac{\partial w}{\partial x}\right]+
\frac{\partial}{\partial y}\left[g(w)\frac{\partial w}{\partial y}\right]$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Exact solutions in implicit form:
$$\displaylines{
x\frac{\sin\varphi(w)}{\sqrt{f(w)}}+y\frac{\cos\varphi(w)}{\sqrt{g(w)}}+t=\psi_1(w),\cr
x\frac{\sin\varphi(w)}{\sqrt{f(w)}}+y\frac{\cos\varphi(w)}{\sqrt{g(w)}}-t=\psi_2(w),\cr}
$$
where $\varphi(w)$, $\psi_1(w)$, and $\psi_2(w)$ are arbitrary functions.
Remarks:\noindent
1.\enspace It is a nonlinear wave equation of general form (for inhomogeneous anisotropic media).

\noindent
2.\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.~310--312).
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 09:57
Edits by author:0

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