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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
$\displaystyle \frac{\partial^2w}{\partial t^2}=
\sum^n_{k=1}\frac{\partial}{\partial x_k}\left[f_k(w)\frac{\partial w}{\partial x_k}\right]$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Exact solutions in implicit form:
$$\displaylines{
\sum^n_{k=1}x_k\varphi_k(w)=\psi_1(w)+t,\cr
\sum^n_{k=1}x_k\varphi_k(w)=\psi_2(w)-t,\cr}
$$
where $\varphi_1(w)$, \dots, $\varphi_{n-1}(w)$, $\psi_1(w)$, and $\psi_2(w)$ are arbitrary functions,
and the function $\varphi_{n}(w)$ is determined by the normalization condition
$$
\sum^n_{k=1}f_k(w)\varphi_k^2(w)=1.
$$
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 10:00
Edits by author:0

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