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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
$\displaystyle \frac{\partial^2 w}{\partial t\partial x}-
\left(\frac 1w\frac{\partial w}{\partial t}+b\right)\frac{\partial w}{\partial x}-\frac{c}{w}\frac{\partial w}{\partial t}-kw-cb= 0$.
%where $b\neq0$, $c$, and $k\neq0$ are constants.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
The general solution:\hfill\break
$\displaystyle w(t,x) =
\left\{-c\int\exp\left(\frac{k}{b^2}[e^{bt}G(x)+bx]\right)dx+F(t)\right\}\exp\left\{-\frac{k}{b^2}[e^{bt}G(x)+bx]\right\}
$,\hfill\break
where $F(t)$ and $G(x)$ are arbitrary functions, and $b\neq0$ and $k\neq0$.
Novelty:Material has been fully published elsewhere
References:Yu.N. Kosovtsov. The general solutions of some nonlinear second and third order PDEs with constant and nonconstant parameters. (2006). http://arxiv.org/abs/math-ph/0609003
Author/Contributor's Details
Last name:Kosovtsov
First name:Yurii
Country:Ukraine
City:Lvov
Statistic information
Submission date:Mon 11 Dec 2006 10:43
Edits by author:0

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