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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:4.1. Second-Order Quasilinear Parabolic Equations
Equation(s):\noindent
$\displaystyle \frac{\partial^2 w}{\partial t^2} +bw \frac{\partial w}{\partial t}+a\frac{\partial w}{\partial x}=0$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Solution:\hfill\break
$\displaystyle w = \frac{\displaystyle 2\int_{-\infty}^\infty\,\omega
F(\omega)\exp\left(-\frac{x(\omega^2+c)}{a}+\omega t\right)\,d\omega}
{\displaystyle b\int_{-\infty}^\infty\,F(\omega)\exp\left(-\frac{x(\omega^2+c)}{a}+\omega
t\right)\,d\omega}$,\hfill\break
where $F(\omega)$ is an arbitrary function, 
$c$ is an arbitrary constant, and $a\neq0$ and $b\neq0$.
Novelty:New solution(s) / integral(s)
Admin's Comment:It is the unnormalized Burgers equation (in other notations, $x\rightleftharpoons t$).
Author/Contributor's Details
Last name:Kosovtsov
First name:Yurii
Country:Ukraine
City:Lvov
Statistic information
Submission date:Thu 07 Dec 2006 11:10
Edits by author:0

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