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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
$\displaystyle \left(\frac{\partial w}{\partial x}\right)^{\!2}\frac{\partial^2 w}{\partial t^2}=
\left(\frac{\partial w}{\partial t}\right)^{\!2}\frac{\partial^2 w}{\partial x^2}+
f(w)\left(\frac{\partial w}{\partial x}\right)^{\!4}$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Solutions:\hfill\break
$\displaystyle x+t\left(\int f(w)\,dw+C_1\right)^{\!1/2}=\varphi(w)$,\hfill\break
$\displaystyle x-t\left(\int f(w)\,dw+C_2\right)^{\!1/2}=\psi(w)$,\hfill\break
where $\varphi(w)$ and $\psi(w)$ are arbitrary functions, 
and $C_1$ and $C_2$ are arbitrary constants.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Thu 07 Dec 2006 09:08
Edits by author:0

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