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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
$\displaystyle \frac{ac}{w}+b+\frac{a}{w}\frac{\partial w}{\partial
x}-\frac{a^2}{w^4}\left(c\frac{\partial w}{\partial t}+\frac{\partial
w}{\partial t}\frac{\partial w}{\partial x}-w\frac{\partial^2
w}{\partial t\partial x}\right)^{\!2}=0$.
%where $a\neq0$, $b$, and $c$ are constants.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
The general solution for $a\neq0$:\hfill\break
$\displaystyle w(t,x) =
 \left\{-c\int
\exp\left[-\frac{1}{4a}\left(-4bx+\int(t+G(x))^2dx\right)\right]\,dx+F(t)\right\}\exp\left[\frac{1}{4a}\left(-4bx+\int(t+G(x))^2dx\right)\right]
$,\hfill\break
where $F(t)$ and $G(x)$ are arbitrary functions.
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 11:23
Edits by author:0

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