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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
$\displaystyle \frac{\partial^2 w}{\partial x\partial y}=\frac{\partial w}{\partial x}f\left(\frac{\partial w}{\partial x}+aw\right)$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Solution:\hfill\break
$\displaystyle w(x,y)=\varphi(y)+C\exp\left[-ax+\int f(a\varphi(y))\,dy\right]$,\hfill\break
where $\varphi(y)$ is an arbitrary function, $C$ is an arbitrary constant.
Novelty:Material has been fully published elsewhere
References:Tsyfra I. Non-local anzatze for nonlinear heat and wave equations. J. Phys. A: Math. Gen., Vol. 30, pp. 2251--2262, 1997.
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Thu 07 Dec 2006 09:21
Edits by author:0

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